Question

In Fig. AB and CD are two equal chords of
a circle with centre 0. OP and OQ are
perpendiculars on chords AB and CD
respectively. If angle POQ = 150°, then angle APQ
is equal to
a) 30°
b) 75°
c) 15°
d) 60°​

Answer 1

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Answer 2

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Since AB=CD (equal chords) so, their distance from centre must le equal.

So, OP=OQ

Now, In △POQ

(1) ∠OPQ=∠OQP

(1) ∠OPQ=∠OQP(2)

∠OPQ+∠OQP+∠POQ=180°

⇒2∠OPQ+150°=180°

⇒∠OPQ=15°

Also, ∵P is midpoint of AB

OP⊥AB⇒∠APO=90°

Now, ∠APQ=∠APO−∠OPQ=90° −15° =75°

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