Fewpal
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Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

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Solution:

Let AB be a diameter of the circle. Two tangents PQ and RS are drawn at points A and B respectively.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel
Radii of the circle to the tangents will be perpendicular to it.
∴ OB ⊥ RS and,

∴ OA ⊥ PQ
∠OBR = ∠OBS = ∠OAP = ∠OAQ = 90º

From the figure,
∠OBR = ∠OAQ (Alternate interior angles)
∠OBS = ∠OAP (Alternate interior angles)
Since alternate interior angles are equal, lines PQ and RS will be parallel.

Hence Proved that the tangents drawn at the ends of a diameter of a circle are parallel.

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