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
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