Question

prove that the line segment joining the points of contact of two parallel tangent passes through the centre.

Answer 1

Here its your answer :



Consider AB and CD are two parallel tangents to the circle.

Consider P and Q be the point of contact and POQ be a line segment.

Construction: Join OP and OQ where O is the centre of a circle.

Proof: OQ ⊥CD and OP ⊥ AB.

Since AB || CD, OP || OQ.

As OP and OQ pass through O,

Hence, POQ is a straight line which passes through the centre of a circle

Consider AB and CD are two parallel tangents to the circle.

Consider P and Q be the point of contact and POQ be a line segment.

Construction: Join OP and OQ where O is the centre of a circle.

Proof: OQ ⊥CD and OP ⊥ AB.

Since AB || CD, OP || OQ.

As OP and OQ pass through O,

Hence, POQ is a straight line which passes through the centre of a circle

Answer 2

$\textbf{Answer is in Attachment !}$