Question

MATHEMAT
4. Prove that the tangents drawn at the ends of a diameter of a circle are parallel
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Answer 1

Let AB be a diameter of the circle. Two tangents PQ and RS are drawn at drawn to these tangents will be points A and B respectively. Radius perpendicular to the tangents. Since alternate interior angles are equal, lines PQ and RS will be 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