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