wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the centre of the circle.

Open in App
Solution

Let AB be the chord of the given circle with centre O and a radius of 10 cm.
Then AB =16 cm and OB = 10 cm

From O, draw OM perpendicular to AB.
We know that the perpendicular from the centre of a circle to a chord bisects the chord.
∴ BM = 162 cm=8 cm
In the right ΔOMB, we have:
OB2 = OM2 + MB2 (Pythagoras theorem)
⇒ 102 = OM2 + 82
⇒ 100 = OM2 + 64
⇒ OM2 = (100 - 64) = 36
OM=36 cm=6 cm
Hence, the distance of the chord from the centre is 6 cm.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Circles and Their Chords - Theorem 3
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon