Question

Prove that tangent drawn at the end of a diameter of a circle are parallel to each other?

Answer 1

Please see the picture to understand the figure. 

Now in the figure, we know that Angle OAP = Angle OBS= 90° (Tangent at any point of a circle is perpendicular to the radius through point of contact)

But Angle OAP = Angle OBS are alternate interior angles. 

Thus PQ║RS

Hence Proved. 

Answer 2

Let AB be a diameter of the circle. Two tangents PQ and RS are drawn at points A and B respectively.

Radius drawn to these tangents will be perpendicular to the tangents.

Thus, OA ⊥ RS and OB ⊥ PQ

∠OAR = 90º

∠OAS = 90º

∠OBP = 90º

∠OBQ = 90º

It can be observed that

∠OAR = ∠OBQ (Alternate interior angles)

∠OAS = ∠OBP (Alternate interior angles)

Since alternate interior angles are equal, lines PQ and RS will be parallel