Question

AB and CD are two equal chords of a circle with centre O and radius 4cm.
If < AOB =660, find the measure of < OCD.

Answer 1

Answer:

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°

Step-by-step explanation:

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