Question

The tangents drawn, at the end-points of a diameter, to a circle are ___________.

Answer 1

AB is the diameter of the circle with centre O. CD and EF are the tangents to the circle at points A and B, respectively.

Now,

∠OAD = 90º (Radius is perpendicular to the tangent at the point of contact)

Also, ∠OBF = 90º (Radius is perpendicular to the tangent at the point of contact)

∴ ∠OAD + ∠OBF = 90º + 90º = 180º

⇒ CD || EF (If a pair of consecutive interior angles is supplementary, then the two lines are parallel)

Hence, the tangents drawn at the end-points of a diameter to a circle are parallel.

The tangents drawn, at the end-points of a diameter, to a circle are __parallel__.