prove that the tangents drawn at the ends of a diameter of a circle are parallel Related: Facts That Matter, Circles - Mathematics for Class 10th

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prove that the tangents drawn at the ends of a diameter of a circle ar...

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 = 90DEG

∠OAS = 90DEG

∠OBP = 90DEG

∠OBQ = 90DEG

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.

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