Q. 114.1( 10 Votes )

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

Answer :


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°


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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