Question

AB and CD are two chords of a circle intersecting at P. Prove that AP x PB = CP x PD

Answer 1

Construction: Join AD and CB.

In ΔAPD and ΔCPB

∠A = ∠C      .....(Angles in the same segment)

∠D = ∠B      .....(Angles in the same segment)

⇒ ΔAPD ~ ΔCPB    ...(By AA Postulate)

`=> (AP)/(CP) = (PD)/(PB)`   ...(Corresponding sides of similar triangles)

`=> AP xx PB = CP xx PD`