Question

O is the centre of the circle as shown in the figure, $\angle ORP={35}^{\circ }$ and the distance between P and Q through 'O' is 4 cm. What is the measure of $\angle ROQ$ ?

• A. ${55}^{\circ }$
• B. ${35}^{\circ }$
• C. ${105}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is D ${70}^{\circ }$

$PQ=4cm=2\times OQ$ $=2\times$ radius, PQ is the diameter of circle.
Join $RQ.\angle PRQ={90}^{\circ }$ $\because$ angle subtended by diameter on the circle is ${90}^{\circ }$
$\therefore \angle ORQ={90}^{\circ }-{35}^{\circ }={55}^{\circ }$
But $OR=OQ$
$\therefore \angle ORQ=\angle OQR={55}^{\circ }$
$\therefore y={180}^{\circ }-({55}^{\circ }+{55}^{\circ })={70}^{\circ }$