MathematicsTwo tangents are drawn to a circle from an external point then they subtend equal angles at the ____.

Two tangents are drawn to a circle from an external point then they subtend equal angles at the ____.

Two tangents are drawn to a circle from an external point then they subtend equal angles at the center.

Let a circle with centre A, CD and CE are tangents to circle.
Join AD and AE.
In

Δ C A D

and

Δ C A E

C D = C E

(Length of the tangents drawn from external point of the circle is equal.)

C A = C A

(common side)

A D = A E

(radius of circle)
Hence,

Δ C A D = Δ C A E

(SSS congruency)
By CPCT,

∠ C A D = ∠ C A E

Hence, two tangents are drawn to a circle from as external point then they subtend equal angles at the centre.

JEE