Question

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

Answer 1

Answer:

Prove that the tangents drawn at the end of a diameter of a circle are parallel. ... Let PQ be the tangent at point A & Rs be the point B. Proof: Since PQ is a tangent at point A. OA⊥ PQ(Tangent at any point of circle is perpendicular to the radius through point of contact).

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.