Question

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

Answer 1

Here, PT and QS are the tangents to the circle with center O and AB is the diameter

Now, radius of a circle is perpendicular to the tangent at the point of contact

∴ OA ⊥ AT and OB ⊥ BS

(Since tangents drawn from an external point are perpendicular to the radius at point of contact)

∴ ∠OAT = ∠OBQ = 90°

But ∠OAT and ∠OBQ are alternate angles.

∴ AT is parallel to BS.