if two intersecting chords of circle make makes eqqqual angles with the diameter passing through their point of intersection.prove that chords are equal.

Hi!
Here is the answer to your question.
 
Given: AB is the diameter of the circle with centre O. AP and AQ are two intersecting chords of the circle such that ∠PAB = ∠QAB.
To prove: AP = AQ
Construction: Draw OL⊥AB and OM⊥AC.
Proof: In ∆AOL and ∆AOM
∠OLA = ∠OMB  (90°)
OA = OA    (Common)
∠OAL = ∠OAM  (∠PAB = ∠QAB)
∴ ∆AOL  ∆AOM    (AAS congruence criterion)
⇒ OL = OM  (C.P.C.T)
⇒ Chords AP and AQ are equidistant from centre O
⇒ AP = AQ  (Chords which are equidistant from the centre are equal)
 
Cheers!

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