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

Let PQ and RS be tangents to the circle at the ends of the diameter AB.

We know that,

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Thus, OA ⊥ PQ and OB ⊥ RS

∴ ∠PAO = 90°, ∠RBO = 90°, ∠OAQ = 90° and ∠OBS = 90°

Here, ∠OAQ is equal to ∠OBR and ∠PAO is equal to ∠OBS, which are two pairs of alternate interior angles.

If the alternate interior angles are equal, then lines PQ and RS should be parallel.

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