We need to prove that the tangents drawn at the ends of a diameter of circle are parallel.
Given circle C(0, r)
AB is diameter. Two tangents PQ and RS drawn at points A and B respectively.
To prove PQ || RS
Proof : Radius will be perpendicular to these tangents
Thus OA ⊥ PQ and OB ⊥ RS
√OAQ = √OAP = √OBS = √OBR = 90°
Therefore √OAQ = √OBR (Alternative interior angles)
√OAP = √OBS (Alternative interior angles)
Since alternate interior angles are equal
:. lines PQ and RS will be parallel.
