If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.
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Step-by-step explanation:
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
Proof:In △AOL and △AOM
∠OLA=∠OMB (each 90
∘
)
OA=OA(common line)
∴∠OAL=∠OAM(∠PAB=∠QAB)
∴△AOL≅△AOM by AAS congruence criterion
⇒OL=OM by CPCT
⇒Chords AP and AQ are equidistant from centre O
⇒AP=AQ(chords which are equidistant from the centre are equal.)
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