Question

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

Answer 1

Answer:

Proved that,

Tangent AB ∥ tangent CD

Step-by-step explanation:

To prove:

Tangent AB ∥ tangent CD

Proof:

In a circle with centre O, OM ⊥ ON are the radii and AB and CD are the tangents respectively.

∴ By the theorem 10.1 which states that tangent at any point of a circle is perpendicular to the radius through the point of contact.

OM ⊥ AB and OM ⊥ OD

∴ ∠OMA = 90° and ∠OND = 90°

∴ ∠OMA = ∴ ∠OND

But, this is a pair of alternate angles,

∴ By alternate angle test for parallel lines,

AB ∥ CD

∴ Tangent AB ∥ tangent CD

Hence, the proof.

Answer 2

Answer:-

Proved that,

Tangent AB ∥ tangent CD

Step-by-step explanation:

To prove:

Tangent AB ∥ tangent CD

Proof:

In a circle with centre O, OM ⊥ ON are the radii and AB and CD are the tangents respectively.

∴ By the theorem 10.1 which states that tangent at any point of a circle is perpendicular to the radius through the point of contact.

OM ⊥ AB and OM ⊥ OD

∴ ∠OMA = 90° and ∠OND = 90°

∴ ∠OMA = ∴ ∠OND

But, this is a pair of alternate angles,

∴ By alternate angle test for parallel lines,

AB ∥ CD

∴ Tangent AB ∥ tangent CD

Hence, the proof.