Question

11.
A
c
P
150°
In Fig. AB and CD are two equal chords of
a circle with centre O. OP and on are
perpendiculars on chords AB and CD
respectively. If ZPOQ = 150°, then ZAFQ
is equal to
a) 30°
b) 75°
c) 15°
d) 60°
D​

Answer 1

Answer:

In the given figure, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD respectively. If ∠ POQ = 120°, find ∠APQ .

Step-by-step explanation:

Since AB = CD

∴ OP = OQ [∵ equal chords are equidistant from the centre]

∴ ∠OPQ = ∠OQP [by using isosceles triangle property, angles opp. to equal sides of a △]

In △POQ, by using angle sum property, we have

∠OPQ + ∠OQP + ∠POQ = 180°

⇒ ∠OPQ + ∠OPQ +120° = 180°

⇒ 2∠OPQ = 60°

⇒∠OPQ = 30°

Now, ∠APQ + ∠OPQ = 90°

⇒ ∠APQ + 30° = 90°

⇒ ∠APQ = 90° - 30° = 60°

Hence, ∠APQ = 60°

Answer 2

Answer:

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