Question

In the picture O is the centre of the circle and A, B, C are points on it. Then $\angle OAC+\angle ABC$ equals ___

• A. ${75}^{\circ }$
• B. ${90}^{\circ }$
• C. ${60}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is B

${90}^{\circ }$

Let $\angle OAC=x$

$\angle OCA=x$

(Since, OC = OA)

Now,

In $\Delta OCA$

$\angle OCA+\angle OAC+\angle AOC={180}^{\circ }$

$x+x+\angle AOC={180}^{\circ }$

$\angle AOC=180-2x$

$\angle B=\frac{1}{2}\angle AOC=\frac{1}{2}(180-2x)$

$=90-x$

So,
$\angle OAC+\angle ABC=90-\text{/}x+\text{/}x={90}^{\circ }$