Question

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

Answer 1

$\angle$OBC = ${90}^{\circ }$ (The tangent at any point of a circle is perpendicular to the radius through the point of contact)

$\angle$OAE = ${90}^{\circ }$ (The tangent at any point of a circle is perpendicular to the radius through the point of contact)

CD $\perp$BA

EF $\perp$ BA

Therefore we can conclude that CD || EF.

Hence proved.