Show that the tangent lines at the end points of a diameter of a circle are parallel.

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

Thus, OA ⊥ EF and OB ⊥ CD

Since the tangents are perpendicular to the radius,

⇒ ∠CBO = 90°, ∠EAO = 90°

⇒ ∠FAO = 90°, ∠OBD = 90°

∴ ∠DBO = ∠OAE, ∠CBO = ∠OAF

These are pair of alternate interior angles.

If the alternate interior angles are equal, then lines CD and EF should be parallel.

CD and EF are the tangents drawn to the circle at the ends of the diameter AB.

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