Question

In the figure O is the centre of the circle, if $\angle$ AOC = ${108}^{\circ }$. Find the ration of $\frac{\angle AOC}{\angle ABC}$

• A. $\frac{6}{7}$
• B. $\frac{3}{7}$
• C. $\frac{1}{4}$
• D. $\frac{4}{7}$

Answer 1

The correct option is A $\frac{6}{7}$

$\angle ADC=\frac{1}{2}\angle AOC$ (angle subtended by the chord at the centre is twice the angle subtended by it at any point on the circle)
$\angle ADC={54}^{\circ }$
$\angle ADC+\angle ABC={180}^{\circ }$ (sum of opposite angles quadrilateral is equal to ${180}^{\circ }$)
$\angle ABC={126}^{\circ }$
$\frac{\angle AOC}{\angle ABC}=\frac{6}{7}$