Question

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

Answer 1

 Here AB is a diameter of the circle with centre O, two tangents PQ and RS drawn at points A and B respectively.

Radius will be perpendicular to these tangents.

Thus, OA ⊥ RS and OB ⊥ PQ

∠OAR = ∠OAS = ∠OBP = ∠OBQ = 90º

Therefore,

∠OAR = ∠OBQ (Alternate interior angles)

∠OAS = ∠OBP (Alternate interior angles)

Since alternate interior angles are equal, lines PQ and RS will be parallel.

Answer 2

Answer:

Hello ,

In the circle , 2 x radius = diameter

we also know , radius ⊥ tangent

then , the diameter forms a straight line with an angle of 180°

So , it is clear that the tangents will be straight and do not meet

∴ They are parallel