Question

$O$ is the centre of the circle as shown in the figure, $\angle ORP=35°$ and the distance between $PandQ$ through $O$ is $4cm$. What is the measure of $\angle ROQ$ ?

• A. $55°$
• B. $35°$
• C. $105°$
• D. $70°$

Answer 1

The correct option is D

$70°$

Step 1: Given data -

As per data given in the question,

Since,$PQ=4cm=2\times OQ$

As, $OQ$ is the radius of the circle.

So,$PQ=2\times$radius,

$PQ$is the diameter of circle.

Step 2: Theorem related to semicircle:

Now we will join $RQ$,

The angle subtended in a semicircle is a right angle.

$$\begin{gathered} \angle PRQ=90° \\ \therefore \angle ORQ=90°-35°=55° \end{gathered}$$

Step 3: Sum of angles of a triangle is$180°$

As we have, $OR=OQ.$

$$\begin{gathered} \therefore \angle ORQ=\angle OQR=55°(Isoscalestriangleproperty) \\ \therefore y=180°-(55°+55°)=70° \end{gathered}$$

Hence, option (D) is the correct choice.