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jai kohli
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Asked: 2023-02-15T07:20:46+00:00 In:

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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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.

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      Two chords AB and CD intersect each other at the point P. Prove that : (i) ∆APC ~ ∆ DPB (ii) AP . PB = CP . DP

      Join CB.
      (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

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