Question

In the given figure, $AB$ is diameter of the circle with centre $O,AQ,BP$ and $PRQ$ are tangents then $OP$ and $OQ$ are perpendicular to each other.

• A. True
• B. False

Answer 1

The correct option is A True

In the above figure first of all join OR

Now, from the figure it is seen that

$\Delta OBP$ is congruent to$\Delta ORP$

Then, $\angle$BOP=$\angle$ROP=x

Now, from the figure it is also seen that

$\Delta$ OAQ is congurent $\Delta$ORQ

$\angle AOQ=\angle ROQ=y$

Since AOB is straight line,

$\angle$AOB=180

$⟹x+x+y+y=180⟹x+y=90⟹\angle POQ={90}^{\circ }$

​ Hence OP and OQ are perpendicular to each other.