Question:
prove that the line segment joininig the points of contact of two parallel tangents passes through the centre
Answer:
Let AB and CD are two parallel tangents to the circle haveing center O.
Let P and Q are the point of contact and POQ is a line segment.
Now, join OP and OQ as shown in the figure.
From the figure,
since AB || CD and OP || OQ
as Op and OQ pass through the center O.
Hence, POQ is a straight line which passes through the center of the circle.
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