Question

Prove that the tangents dawn an external point to a circle are equal

Answer 1

Answer:

Hope its helpful.....

Answer 2

Hi mate here is the answer:--✍️✍️

Question:✔️

Prove that the length of tangents drawn from an external point to a circle are equal.

Solution:✔️

Let’s take PQ and PR, are the tangents drawn from an external point P to a circle with centre O.

To prove:

PR = PQ

Construction:

Join O to P, R and Q

It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.

OR ⟘ PR and OQ ⟘ PQ ... (i)

Proof: In ∆ORP and ∆OQP

OR = OQ (Radius of same circle)

OP = OP (Common)

∠ORP = ∠OQP (Each 90°)

∴ ∆ORP ≅ ∆OQP (R.H.S)

∴ PR = PQ

Corresponding parts of congruent triangles are equal.

Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.

Hope it helps you ❣️☑️☑️