Question

Find the length of a chord which is at a distance of 15 cm from the centre of a circle of radius 25 cm.

Answer 1

Let AB be the chord with distance OC = 15cm from the center and radius = 25cm.

Then, we have, $OC\perp AB$ and hence $AC=CB=AB/2$.....(perpendicular drawn from the centre of the circle to the chord ,bisects the chord)

Then using Pythagorean formula for $\Delta OAC$ we get :

$AC=\sqrt{(O{A}^2-O{C}^2)}=\sqrt{({25}^2-{15}^2)}=\sqrt{400}=20cm$