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

In the given ...

Question

In the given figure, AB is the diameter of the circle with centre O.

If $∠ A D C = 32^{\circ},$ find angle BOC.

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Solution

$\widehat{AC}$ subtends $AOC$ at the center and $ADC$ at the circumference of the circle.

$\angle AOC = 2 \angle ADC$

$\Rightarrow \angle AOC = 2 \times 32 = 64^o$

$\angle AOC + \angle BOC = 180 \Rightarrow \angle BOC = 180-64=116^o$

$\\$

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