# Prove that the tangents drawn at the ends of the diameter of a circle are parallel.

Let AB be the diameter of a circle with center O.

CD and EF are two tangents at ends A and B respectively.

To Prove : CD || EF

Proof :

OA CD and OB EF

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

OAD + OBE = 90° + 90° = 180°

Considering AB as a transversal

CD || EF

[Two sides are parallel, if any pair of the interior angles on the same sides of transversal is supplementary]

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