Question

prove that tangents drawn at the ends of a diameter of a circle are parallel ​

Answer 1

Step-by-step explanation:

Radius through point of contact is perpendicular to tangent and therefore diameter is subtends 90° with tangent......

So by alternate interior angle property tangents are parallel...

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