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