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

Let PQ be a diameter of the given circle with centre O.

Let AB and CD be the tangents drawn to the circle at the end points of the diameter PQ respectively.

$$\therefore$$ Tangent at a point to a circle is perpendicular to the radius through the point,

$$\therefore$$ $$PQ \ ⊥ \ AB$$ and $$PQ \ ⊥ \ CD$$

$$\Rightarrow \ ∠ \ APQ \ = \ ∠ \ PQD$$

$$\Rightarrow \ AB \ || \ CD$$ [$$\because$$ $$∠ \ APQ$$ and $$∠ \ PQD$$ are alternate angles]

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