A circle with a diameter AB

PQ is a tangent drawn at A and RS is a tangent drawn at B

R.T.P: PQ // RS

Proof Let 'O' be the center of the circle then is radius and PQ is a tangent

OA ⟂ --------(1)

[ a tangent drawn at the end point of the radius is perpendicular to the radius]

similarly ⟂ RS -------(2)

[a tangent drawn at the end point of the radius is perpendicular to the radius]

But, OA and OB are the parts of

i.e., AB ⟂ and AB ⟂

PQ ∥ RS

O is the center, PQ is a tangent drawn at A

∠OAQ = °

Similarly ∠OBS = 90°

∠OAQ + ∠OBS = ° + ° = °

∴ PQ ∥ RS

[∵ Sum of the consecutive interior angles is 180°, hence lines are parallel]