In the figure $ P O \perp Q 0 $. The tangents to the circle at $ P $ and $ Q $ intersect at a point $ T $. Prove that $ P Q $ and $ O T $ are right bisectors of each other."

Given:

In the figure \( P O \perp Q 0 \). The tangents to the circle at \( P \) and \( Q \) intersect at a point \( T \).

To do:
We have to prove that \( P Q \) and \( O T \) are right bisectors of each other.

 Solution:

$PT$ and $QT$ are tangents to the circle.

$PT = QT$

$PO\ \perp\ QO$

$OP$ and $OQ$ are radii of the circle and $\angle POQ = 90^o$

$OQTP$ is a square where $PQ$ and $OT$ are diagonals.

Diagonals of a square bisect each other at right angles.

$PQ$ and $OT$ bisect each other at right angles.

Therefore, $PQ$ and $QT$ are right bisectors of each other.

Hence proved.

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Updated on: 10-Oct-2022

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