Q. 114.1( 10 Votes )
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
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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