Question 7:
In the given figure, two chords AB and CD intersect each other at the point P. prove that:
(i) ΔAPC ∼ ΔDPB (ii) AP.BP = CP.DP
Answer:
Let us join CB.
(i) In ΔAPC and ΔDPB,
∠APC = ∠DPB (Vertically opposite angles)
∠CAP = ∠BDP (Angles in the same segment for chord CB)
ΔAPC ∼ ΔDPB (By AA similarity criterion)
(ii) We have already proved that
ΔAPC ∼ ΔDPB
We know that the corresponding sides of similar triangles are proportional.
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