In the given figure, $O$ is the centre of a circle, $B C$ is its chord and $A$ is any point on the circle. If $∠ B A C = a$ and $∠ O B C = b$ , find $a + b$ .

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Solution

$\begin{matrix} I n c i r c l e O B = O C = r a d i u s ∠ O = 2 ∠ A = 29^{\circ} a n g l e a t c e n t r e i s t w i c e o f a n g l e a t c i r c u m f e r e n c e S u m o f a n g l e o f Δ O B C ∠ O P C + ∠ O C B + 29 = 180^{\circ} 29 + 2 b = 180^{\circ} a + b = 90^{\circ} \end{matrix}$

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