Geometry Questions for SSC CGL, CHSL

Geometry Objective Questions with Solution for SSC CGL, CHSL Competitive Exams. All type MCQs Mock Test for online practice.

Quiz : Geometry
Subject : Mathematics
Medium : English
Important questions with answer from previous year SSC papers
Solution with Short tricks

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Results

#1. The centroid of an equilateral triangle ABC is G and AB is 10 cm. The length of AG (in cm) is

$3\frac13$

$\frac{10}{\sqrt3}$

$\frac{10\sqrt3}{3}$

$\frac{\sqrt3}{3}$

#2. The side BC of a triangle ABC is extended to D. If $\angle ACD = 120°$ and $\angle ABC = \frac{1}{2} \angle CAB$ , then the value of $\angle ABC$ is

80°

40°

60°

20°

#3. The side BC of a triangle ABC is extended to D. If $\angle ACD = 120°$ and $\angle ABC = \frac{1}{2} \angle CAB$ , then the value of $\angle ABC$ is

80°

40°

60°

20°

#4. In a triangle, if three altitudes are equal, then the triangle is :

Obtuse

Equilateral

Right

Isosceles

Explanation: Triangle will be equilateral.
Hence, the correct option is

#5. The in-radius of an equilateral triangle is of length 3 cm. Then the length of each of its medians is

12 cm

$\frac92$ cm

4 cm

9 cm

#6. ABC is an isosceles triangle such that AB = AC and AD is the median to the base BC with ∠ABC = 35°. Then ∠BAD is

35°

55°

70°

110°

#7. If angle bisector of a triangle bisects the opposite side, then what type of triangle is it?

Right-angled

Scalene

Similar

Isosceles

#8. In a triangle $ABC, AB = AC, \angle BAC = 40^\circ$ Then the external angle at B is :

$90^\circ$

$70^\circ$

$110^\circ$

$80^\circ$

#9. In a triangle $ABC, AB = AC, \angle BAC = 40^\circ$ Then the external angle at B is :

$90^\circ$

$70^\circ$

$110^\circ$

$80^\circ$

#10. ABC is a triangle and the sides AB, BC and CA are produced to E, F and G respectively. If $\angle CBE = \angle ACF = 130^\circ$ then the value of $\angle GAB$ is

100°

130°

80°

90°

#11. ABC is a triangle and the sides AB, BC and CA are produced to E, F and G respectively. If $\angle CBE = \angle ACF = 130^\circ$ then the value of $\angle GAB$ is

100°

130°

80°

90°

#12. In $∆ABC \angle B = 60°, and \angle C = 40^\circ$ , AD and AE are respectively the bisector of $\angle A$ and perpendicular on BC. The measure of $\angle EAD$ is

$11^\circ$

$10^\circ$

$12^\circ$

$9^\circ$

#13. In $∆ABC \angle B = 60°, and \angle C = 40^\circ$ , AD and AE are respectively the bisector of $\angle A$ and perpendicular on BC. The measure of $\angle EAD$ is

$11^\circ$

$10^\circ$

$12^\circ$

$9^\circ$

#14. The side BC of a triangle ABC is produced to D. If $\angle ACD = 112^\circ$ and $\angle B =\frac {3}{4} \angle A$ , then the measure of $\angle B$

30°

48°

45°

64°

#15. The side BC of a triangle ABC is produced to D. If $\angle ACD = 112^\circ$ and $\angle B =\frac {3}{4} \angle A$ , then the measure of $\angle B$

30°

48°

45°

64°

#16. A man goes 24 m due west and then 10 m due north. Then the distance of him from the starting point is

17 m

26 m

28 m

34 m

#17. In $∆ABC, \angle B = 60°,\angle C = 40^\circ, AD$ is the bisector of $\angle A$ and AE is drawn perpendicular on BC from A. Then the measure of $\angle EAD$ is

40°

30°

10°

80°

#18. In $∆ABC, \angle B = 60°,\angle C = 40^\circ, AD$ is the bisector of $\angle A$ and AE is drawn perpendicular on BC from A. Then the measure of $\angle EAD$ is

40°

30°

10°

80°

#19. I is the incentre of $∆ABC, \angle ABC = 60^\circ$ and $\angle ACB = 50^\circ$ . Then $\angle BIC$ is

$55^\circ$

$125^\circ$

$70^\circ$

$65^\circ$

#20. I is the incentre of $∆ABC, \angle ABC = 60^\circ$ and $\angle ACB = 50^\circ$ . Then $\angle BIC$ is

$55^\circ$

$125^\circ$

$70^\circ$

$65^\circ$

#21. If the sides of a triangle are in the ratio $3 : 1\frac{1}{4}: 3\frac{1}{4}$ then the triangle is .

Right triangle

Obtuse triangle

Equiangular triangle

Acute triangle

#22. If the sides of a triangle are in the ratio $3 : 1\frac{1}{4}: 3\frac{1}{4}$ then the triangle is .

Right triangle

Obtuse triangle

Equiangular triangle

Acute triangle

#23. In ∆ABC, ∠B = 90°, AB = 8 cm and BC = 15 cm, then sin C = ?

$\frac{15}{17}$

$\frac{8}{17}$

$\frac{15}{8}$

$\frac{8}{15}$

#24. If the sides of a right angled triangle are three consecutive integers, then the length of the smallest side is

3 units

2 units

4 units

5 units

#25. In a ∆ABC, D and E are two points on AB and AC respectively such that DE || BC, DE bisects the ∆ABC in two equal areas. Then the ratio of DB : AB is

$1 : \sqrt2$

1 : 2

$(\sqrt2 – 1) : \sqrt2$

$\sqrt2 : 1$

#26. The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then AB is

15 cm

12 cm

14 cm

26 cm

#27. Inside a square ABCD, ∆ BEC is an equilateral triangle. If CE and BD intersect at O, then ∠BOC is equal to

60°

75°

90°

120°

#28. The measure of each interior angle of a regular polygon with 8 sides is

135°

120°

100°

45°

#29. The sum of interior angles of a regular polygon is 1440° The number of sides of the polygon is

#30. The sum of all internal angles of a regular polygon whose one external angle is 20° is

6400°

3200°

2880°

1440°

#31. The number of sides in two regular polygons are in the ratio 5 : 4 and the difference between each interior angle of the polygons is 6°. Then the number of sides is :

15, 12

5, 4

10, 8

20, 16

#32. The length of the diagonal BD of the parallelogram ABCD is 18 cm. If P and Q are the centroid of the ∆ABC and ∆ADC respectively then the length of the line segment PQ is :

4 cm

6 cm

9 cm

12 cm

#33. The point of intersection of the diagonals AC and BD of the cyclic quadrilateral ABCD is P. If $\angle APB = 64^\circ$ and $\angle CBD = 28^\circ$ . The measure of $\angle ADB$ is

32°

36°

56°

28°

#34. The point of intersection of the diagonals AC and BD of the cyclic quadrilateral ABCD is P. If $\angle APB = 64^\circ$ and $\angle CBD = 28^\circ$ . The measure of $\angle ADB$ is

32°

36°

56°

28°

#35. AB is a diameter of a circle having centre at O. PQ is a chord which does not intersect AB. Join AP and BQ. If $\angle BAP = \angle ABQ$ , then ABQP is a

Cyclic square

Cyclic trapezium

Cyclic rhombus

Cyclic rectangle

#36. AB is a diameter of a circle having centre at O. PQ is a chord which does not intersect AB. Join AP and BQ. If $\angle BAP = \angle ABQ$ , then ABQP is a

Cyclic square

Cyclic trapezium

Cyclic rhombus

Cyclic rectangle

#37. Three circles of radius 6 cm each touch each other externally. Then the distance of the centre of one circle from the line joining the centres of other two circles is equal to

$6\sqrt5$ cm

$6\sqrt3$ cm

$6\sqrt2$ cm

$6\sqrt7$ cm

#38. Two circles having radii r units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is

$\sqrt2 r $ units

$\sqrt2 r$ units

r units

#39. The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is

6 cm

7 cm

8 cm

5.5 cm

#40. Two circles with their centres at O and P and radii 8 cm and 4 cm respectively touch each other externally. The length of their common tangent is

8.5 cm

$\frac{8}{\sqrt2}$ cm

$8\sqrt2$ cm

8 cm

#41. If AB = 5 cm, AC = 12 cm and AB ⊥ AC, then the radius of the circumcircle of ∆ABC is

6.5 cm

6 cm

5 cm

7 cm

#42. The ratio of circumradius and radius of an equilateral triangle is

1 : 2

3 : 1

2 : 1

1 : 3

#43. A tree of hight ‘h’ metres is broken by a storm in such a way that it’s top touches the ground at a distance of ‘x’ metres from its root. Find the height at which the tree is broken. (Here $h > x)$

$\frac{h^2 + x^2}{2h}$ metre

$\frac{h^2 – x^2}{2h}$ metre

$\frac{h^2 + x^2}{4h}$ metre

$\frac{h^2 – x^2}{2h}$ metre

#44. A and B are centres of two circles of radii 11 cm and 6 cm respectively. PQ is a direct common tangent to the circles. If $\overline {AB}$ = 13 cm, then the length of $\overline {PQ}$ will be

8.5 cm

13 cm

12 cm

17 cm

#45. A and B are centres of two circles of radii 11 cm and 6 cm respectively. PQ is a direct common tangent to the circles. If $\overline {AB}$ = 13 cm, then the length of $\overline {PQ}$ will be

8.5 cm

13 cm

12 cm

17 cm

FINISH

Results

#1. The centroid of an equilateral triangle ABC is G and AB is 10 cm. The length of AG (in cm) is

#2. The side BC of a triangle ABC is extended to D. If and , then the value of is

#3. The side BC of a triangle ABC is extended to D. If and , then the value of is

#4. In a triangle, if three altitudes are equal, then the triangle is :

#5. The in-radius of an equilateral triangle is of length 3 cm. Then the length of each of its medians is

#6. ABC is an isosceles triangle such that AB = AC and AD is the median to the base BC with ∠ABC = 35°. Then ∠BAD is

#7. If angle bisector of a triangle bisects the opposite side, then what type of triangle is it?

#8. In a triangle Then the external angle at B is :

#9. In a triangle Then the external angle at B is :

#10. ABC is a triangle and the sides AB, BC and CA are produced to E, F and G respectively. If then the value of is

#11. ABC is a triangle and the sides AB, BC and CA are produced to E, F and G respectively. If then the value of is

#12. In , AD and AE are respectively the bisector of and perpendicular on BC. The measure of is

#13. In , AD and AE are respectively the bisector of and perpendicular on BC. The measure of is

#14. The side BC of a triangle ABC is produced to D. If and , then the measure of

#15. The side BC of a triangle ABC is produced to D. If and , then the measure of

#16. A man goes 24 m due west and then 10 m due north. Then the distance of him from the starting point is

#17. In is the bisector of and AE is drawn perpendicular on BC from A. Then the measure of is

#18. In is the bisector of and AE is drawn perpendicular on BC from A. Then the measure of is

#19. I is the incentre of and . Then is

#20. I is the incentre of and . Then is

#21. If the sides of a triangle are in the ratio then the triangle is .

#22. If the sides of a triangle are in the ratio then the triangle is .

#23. In ∆ABC, ∠B = 90°, AB = 8 cm and BC = 15 cm, then sin C = ?

#24. If the sides of a right angled triangle are three consecutive integers, then the length of the smallest side is

#25. In a ∆ABC, D and E are two points on AB and AC respectively such that DE || BC, DE bisects the ∆ABC in two equal areas. Then the ratio of DB : AB is

#26. The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then AB is

#27. Inside a square ABCD, ∆ BEC is an equilateral triangle. If CE and BD intersect at O, then ∠BOC is equal to

#28. The measure of each interior angle of a regular polygon with 8 sides is

#29. The sum of interior angles of a regular polygon is 1440° The number of sides of the polygon is

#30. The sum of all internal angles of a regular polygon whose one external angle is 20° is

#31. The number of sides in two regular polygons are in the ratio 5 : 4 and the difference between each interior angle of the polygons is 6°. Then the number of sides is :

#32. The length of the diagonal BD of the parallelogram ABCD is 18 cm. If P and Q are the centroid of the ∆ABC and ∆ADC respectively then the length of the line segment PQ is :

#33. The point of intersection of the diagonals AC and BD of the cyclic quadrilateral ABCD is P. If and . The measure of is

#34. The point of intersection of the diagonals AC and BD of the cyclic quadrilateral ABCD is P. If and . The measure of is

#35. AB is a diameter of a circle having centre at O. PQ is a chord which does not intersect AB. Join AP and BQ. If , then ABQP is a

#36. AB is a diameter of a circle having centre at O. PQ is a chord which does not intersect AB. Join AP and BQ. If , then ABQP is a

#37. Three circles of radius 6 cm each touch each other externally. Then the distance of the centre of one circle from the line joining the centres of other two circles is equal to

#38. Two circles having radii r units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is

#39. The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is

#40. Two circles with their centres at O and P and radii 8 cm and 4 cm respectively touch each other externally. The length of their common tangent is

#41. If AB = 5 cm, AC = 12 cm and AB ⊥ AC, then the radius of the circumcircle of ∆ABC is

#42. The ratio of circumradius and radius of an equilateral triangle is

#43. A tree of hight ‘h’ metres is broken by a storm in such a way that it’s top touches the ground at a distance of ‘x’ metres from its root. Find the height at which the tree is broken. (Here

#44. A and B are centres of two circles of radii 11 cm and 6 cm respectively. PQ is a direct common tangent to the circles. If = 13 cm, then the length of will be

#45. A and B are centres of two circles of radii 11 cm and 6 cm respectively. PQ is a direct common tangent to the circles. If = 13 cm, then the length of will be

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#2. The side BC of a triangle ABC is extended to D. If $\angle ACD = 120°$ and $\angle ABC = \frac{1}{2} \angle CAB$ , then the value of $\angle ABC$ is

#3. The side BC of a triangle ABC is extended to D. If $\angle ACD = 120°$ and $\angle ABC = \frac{1}{2} \angle CAB$ , then the value of $\angle ABC$ is

#8. In a triangle $ABC, AB = AC, \angle BAC = 40^\circ$ Then the external angle at B is :

#9. In a triangle $ABC, AB = AC, \angle BAC = 40^\circ$ Then the external angle at B is :

#10. ABC is a triangle and the sides AB, BC and CA are produced to E, F and G respectively. If $\angle CBE = \angle ACF = 130^\circ$ then the value of $\angle GAB$ is

#11. ABC is a triangle and the sides AB, BC and CA are produced to E, F and G respectively. If $\angle CBE = \angle ACF = 130^\circ$ then the value of $\angle GAB$ is

#12. In $∆ABC \angle B = 60°, and \angle C = 40^\circ$ , AD and AE are respectively the bisector of $\angle A$ and perpendicular on BC. The measure of $\angle EAD$ is

#13. In $∆ABC \angle B = 60°, and \angle C = 40^\circ$ , AD and AE are respectively the bisector of $\angle A$ and perpendicular on BC. The measure of $\angle EAD$ is

#14. The side BC of a triangle ABC is produced to D. If $\angle ACD = 112^\circ$ and $\angle B =\frac {3}{4} \angle A$ , then the measure of $\angle B$

#15. The side BC of a triangle ABC is produced to D. If $\angle ACD = 112^\circ$ and $\angle B =\frac {3}{4} \angle A$ , then the measure of $\angle B$

#17. In $∆ABC, \angle B = 60°,\angle C = 40^\circ, AD$ is the bisector of $\angle A$ and AE is drawn perpendicular on BC from A. Then the measure of $\angle EAD$ is

#18. In $∆ABC, \angle B = 60°,\angle C = 40^\circ, AD$ is the bisector of $\angle A$ and AE is drawn perpendicular on BC from A. Then the measure of $\angle EAD$ is

#19. I is the incentre of $∆ABC, \angle ABC = 60^\circ$ and $\angle ACB = 50^\circ$ . Then $\angle BIC$ is

#20. I is the incentre of $∆ABC, \angle ABC = 60^\circ$ and $\angle ACB = 50^\circ$ . Then $\angle BIC$ is

#21. If the sides of a triangle are in the ratio $3 : 1\frac{1}{4}: 3\frac{1}{4}$ then the triangle is .

#22. If the sides of a triangle are in the ratio $3 : 1\frac{1}{4}: 3\frac{1}{4}$ then the triangle is .

#33. The point of intersection of the diagonals AC and BD of the cyclic quadrilateral ABCD is P. If $\angle APB = 64^\circ$ and $\angle CBD = 28^\circ$ . The measure of $\angle ADB$ is

#34. The point of intersection of the diagonals AC and BD of the cyclic quadrilateral ABCD is P. If $\angle APB = 64^\circ$ and $\angle CBD = 28^\circ$ . The measure of $\angle ADB$ is

#35. AB is a diameter of a circle having centre at O. PQ is a chord which does not intersect AB. Join AP and BQ. If $\angle BAP = \angle ABQ$ , then ABQP is a

#36. AB is a diameter of a circle having centre at O. PQ is a chord which does not intersect AB. Join AP and BQ. If $\angle BAP = \angle ABQ$ , then ABQP is a

#43. A tree of hight ‘h’ metres is broken by a storm in such a way that it’s top touches the ground at a distance of ‘x’ metres from its root. Find the height at which the tree is broken. (Here $h > x)$

#44. A and B are centres of two circles of radii 11 cm and 6 cm respectively. PQ is a direct common tangent to the circles. If $\overline {AB}$ = 13 cm, then the length of $\overline {PQ}$ will be

#45. A and B are centres of two circles of radii 11 cm and 6 cm respectively. PQ is a direct common tangent to the circles. If $\overline {AB}$ = 13 cm, then the length of $\overline {PQ}$ will be