Q. 1

Prove that the line

Answer :

                                       
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.
∴ ∠ XAO = 90°
and ∠ YBO = 90°
Since ∠ XAO + ∠ YBO = 180°
Angles 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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