Two equal chords AB and CD are drawn in a circle with centre O. Show that A ABC and ACD are congruent.
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Answer:
Since AB=CD (equal chords) so, their distance from centre must le equal
So, OP=OQ
Now, In △POQ
(1) ∠OPQ=∠OQP
(2) ∠OPQ+∠OQP+∠POQ=1800
⇒2∠OPQ+1500=1800
⇒∠OPQ=150
Also, ∵P is midpoint of AB
OP⊥AB⇒∠APO=900
Now, ∠APQ=∠APO−∠OPQ=900−150=750
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