In a circle of radius 10cm, a chord of length 16 cm is drawn. Find the distance from the center of the circle to the chord.
In a circle of radius 10cm, a chord of length 16 cm is drawn. Find the distance from the center of the circle to the chord.
त्रिज्या 10 सेमी वाले एक वृत्त में 16 सेमी लंबाई का एक स्पर्श रेख खींचा गया है। वृत्त के केंद्र से उस स्पर्श रेख तक की दूरी ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
6 cm / 6 सेंटीमीटर
Given:
Radius $r = 10$ cm
Chord length $AB = 16$ cm
Let the distance from the center to the chord be $d$. Draw a perpendicular from the center $O$ to the chord; it bisects the chord.
Half of the chord = $8$ cm
Using Pythagoras theorem in right triangle formed by radius, half chord, and perpendicular distance:
$d^2 + 8^2 = 10^2$
$d^2 + 64 = 100$
$d^2 = 36$
d = 6 cm
✅ Distance from center to chord = 6 cm
Similar Practice Questions
Given is a circle with centre at C. A, B and D are the points on the circumference. Find ∠ABC.
Given is a circle with centre at C. A, B and D are the points...
A regular rights pyramid has a square base with a side length of 12 cm. Its slant height is 8 cm. what is its volume?
A regular rights pyramid has a square base with a side length of 12 cm....
A square field has a diagonal of $\surd98$ m. What is its area?
A square field has a diagonal of $\surd98$ m. What is its area? एक वर्गाकार...
If the curved surface area of a cylindrical pipe is 44,000 cm
If the curved surface area of a cylindrical pipe is 44,000 cm\(^2\) and its diameter...
If a = 0.02, b = 0.03, c = -0.05, and a + b + c = 0, find (a^3 +b^3 + c^3) \div (3abc)
If a = 0.02, b = 0.03, c = -0.05, and a + b +...
The total area of a piece of square glass is 784 cm \(^2\), which is placed on top of a table. The width between the edge of the table and the piece of glass is 9 cm wide. Find the length of the table.
The total area of a piece of square glass is 784 cm \(^2\), which is...
The perimeter of a rectangular garden is 48 m. If the length is 6 m more than the breadth, the are area (in m ^ 2) of the garden is:
The perimeter of a rectangular garden is 48 m. If the length is 6 m...