Question

Prove that the line segment joining the points of contact of two parallel tangent of a circle, passes through its centre.

Answer 1

REF.Image.

We have to prove the line segment joining the point of

contact of two parallel tangents of a circle passes

through its centre.

$\to$ consider $AB$ & $CD$ are two tangents of circle

$\to$ consider $P$ & $Q$ are a point of the intersection of tangents at circle and $POQ$ is a line segment.

${\to }^{\prime }{O}^{\prime }$ is the centre of the circle

$OQ\perp CD;OP\perp AB$

$AB\parallel CD;OP\parallel OQ.\to$ $OP$ & $OQ$ passes through $O$

Hence $POQ$ is a line passes through the centre of the circle