Suppose CD and AB are two parallel tangents of a circle with center O
Construction: Draw a line parallel to CD passing through O i.e. OP
We know that the radius and tangent are perpendicular at their point of contact.
\(\angle\)OQC = \(\angle\)ORA = \(90^\circ\)
Now, \(\angle\)OQC + \(\angle\)POQ = \(180^\circ\) (co-interior angles)
\(\Rightarrow\) \(\angle\)POQ = \(180^\circ\) - \(90^\circ\) = \(90^\circ\)
Similarly, Now, \(\angle\)ORA + \(\angle\)POR = \(180^\circ\) (co-interior angles)
Hence, QR is a straight line passing through center O.