Question

The tangent drawn at the end point of two pependicular diameter of a circle. prove that PQ and RS are parallel

Answer 1

Here AB is a diameter of the circle with centre O, two tangents PQ and RS drawn at points A and B respectively.

Radius will be perpendicular to these tangents.

Thus, OA ⊥ RS and OB ⊥ PQ

∠OAR = ∠OAS = ∠OBP = ∠OBQ = 90º

Therefore,

∠OAR = ∠OBQ(Alternate interior angles)

∠OAS = ∠OBP (Alternate interior angles)

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