Question

Show that the line segment joining the points of contact of two parallel tangents passes through the centre.

Answer 1

To prove: POQ is a diameter of the circle.

Construction: Join OP and OQ.

Draw OE || CD

Proof: OE || CD and PO cuts them.

∴ $\angle$EOQ + $\angle$EOP = 180°

⇒ 90° + $\angle$EOP = 180°

⇒ $\angle$ EOP = 90°

Similarly, $\angle$EOQ = 90°

Therefore, EOP + EOQ = (90° + 90°) = 180°

⇒ POQ is a straight line

Hence, POQ is a diameter of the circle with center O.