Question

show that tangent lines at the point of a diameter of a circle are parallel.​

Answer 1

Step-by-step explanation:

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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 perpendicular RS and OB perpendicular PQ.

∠OAR = 90°

∠OAS = 90°

∠OBP = 90°

∠OBQ = 90°

It can be observed that

∠OAR = 2OBQ (Alternate interior angles)

∠OAS = 2OBP (Alternate interior angles)

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