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.