Prove that the segment joining the point of contact of two parallel tangents passes through the centre.

Explanation

Let AOB is a straight line passing through O

Let PAQ and RBS be two parallel tangents to the circle having centre O

Join OA and OB

`/_PAO=90^0 `tangent to the circle is perpendicular to the radius through the point of contact )

Draw `OC||PA`

`:. /_PAO+/_COA=180^0 `(sum of the angle on the same side of a transversal is 180^0)

`:.90^0 +/_COA=180^0`

`:. /_COA=90^0 `

...