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

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)

  • 20
What are you looking for?