Question

P is the centre of the circle and its radius is
10 cm. Distance of a chord AB from the centre is 6 cm. Find the length of chord AB.

Answer 1

seg PM ⊥ chord AB
In right angled triangle Δ APM
AM² + PM² = AP² ........ (by Pythagoras theorem)
∴ AM² + 6² = 10²
∴ AM² = 100 - 36                                                              
∴ AM² = 64
∴ AM = 8 cm                                                      

We know perpendicular from centre bisects the chord so AM = MB
∴ AB = 2 × AM
∴ AB = 2 × 8
∴ AB = 16 cm
∴ lenght of chord AB = 16 cm.