Question

In the given figure, O is the centre of the circle and A, B, C

are points on it, then $\angle OAC+\angle ABC=$___.

• A. ${60}^{\circ }$
• B. ${70}^{\circ }$
• C. ${90}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is C

${90}^{\circ }$

Join OC

Let $\angle OAC$= x ......(1)

$\therefore \angle OCA=x$ (since, OC = OA)

In $\Delta OCA$

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

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

$\angle AOC$= 180 - 2x

$\angle B=\frac{1}{2}\angle AOC=\frac{1}{2}(180-2x)=90-x$.....(ii)

From (i) & (ii)

$\angle ABC=90-x$

$\angle ABC=90-\angle OAC$

$\angle ABC+\angle OAC={90}^{\circ }$