XY and MN are the tangents drawn at the end points of the diameter DE of the circle with centre O. Prove that XY ∥ MN.
Given: XY & MN are tangents
DE is the diameter
To prove: XY ∥ MN
Proof:
Since Tangent is perpendicular to radius
For lines XY and MN
With transversal DE
∠ YDE = ∠ NED
Thus, alternate interior angles are equal
∴ Lines must be parallel
Hence, XY ∥ MN
Hence proved

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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