Question

In a circle with centre P, a chord of length 16 cm is at a distance of 8 cm from the centre. Find the radius of this circle.

Answer 1

In the given circle, length of the chord is 16 cm and distance of the chord AB from the centre is 8 cm.
Seg AM = Seg MB (Perpendicular drawn from the centre to a chord bisects the chord)


Using Pythagoras Theorem in triangle PAM, we get:
AM² + PM² = PA²
⇒ PA² = 64+ 64
⇒ PA = $\sqrt{128}$ cm
The radius of the circle is $\sqrt{128}$ cm.