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Angle Subtended by an Arc of a Circle on the Circle and at the Center

The figure gi...

Question

The figure given below, shows a circle with centre O.

Given : $∠$ AOC = a and $∠$ ABC = b.

(i) Find the relationship between a and b.

(ii) Find the measure fo angle OAB, if OABC is a parallelogram.

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Solution

(Angle at the centre is double the angle at the circumference subtended by the same chord)

(ii) Since OABC is a parallelogram, so opposite angles are equal

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