Prove the corresponding angles of the two triangles are equal.
How prove the are opposite angles of the intersection point.
Class 10th Maths, Page No:153, chapter Triangles Solutions, Exercise 6.6, Questions No:7.
NCERT Books for 2022-2023 are based on CBSE Board.
Two chords AB and CD intersect each other at the point P. Prove that : (i) ∆APC ~ ∆ DPB (ii) AP . PB = CP . DP
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(i) In ΔAPC and ΔDPB,
∠APC = ∠DPB [Vertically Opposite Angles]
∠CAP = ∠BDP [Angles in the same segment]
ΔAPC ∼ ΔDPB [AA similarity]
(ii) We have already proved that ΔAPC ∼ ΔDPB.
We know that the corresponding sides of similar triangles are proportional. So,
AP/DP = PC/PB = CA/BD ⇒ AP/DP = PC/PB ⇒ AP . PB = PC . DP