Question

Match the column I with column II for the given image below.

• A. ${90}^{\circ }$
• B. ${65}^{\circ }$
• C. $4$

Answer 1

Here, $PR=RQ$ so $R$ is the mid point of $PQ.$

We know that, the line joining the center of a circle to the mid-point of a chord is perpendicular to the chord.
$\therefore \angle R={90}^{\circ }$
Using sum angle property in $△OPR$
$\angle P+\angle R+\angle O={180}^{\circ }\Rightarrow \angle P+{90}^{\circ }+{25}^{\circ }={180}^{\circ }\Rightarrow \angle P={180}^{\circ }-{90}^{\circ }-{25}^{\circ }\Rightarrow \angle P={65}^{\circ }$


$PQ=PR+RQ=2+2=4$ units