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Prove that line segment joining points …

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Prove that line segment joining points of contact of two parallel tangent pass through center

Posted by Pratheeka S U 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Given: l and m are the tangent to a circle such that l || m, intersecting at A and B respectively.
To prove: AB is a diameter of the circle.
Proof:
A tangent at any point of a circle is perpendicular to the radius through the point of contact.
{tex}\therefore{/tex} {tex}\angle X A O = 90 ^ { \circ }{/tex}
and {tex}\angle Y B O = 90 ^ { \circ }{/tex}
Since {tex}\angle X A O + \angle Y B O = 180 ^ { \circ }{/tex}
An angle on the same side of the transversal is 180°.
Hence the line AB passes through the centre and is the diameter of the circle.

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