Question

Two tangents to a circle are inclined at 60 the radius of the circle is 5 cm find the length of the tangent

Answer 1

Step-by-step explanation:

answer are in images please go through them

Answer 2

Given:-

Angle between tangents to a circle from an external point is 60°.Radius of circle i.e OP = OQ = 5cm

$\underline\bold\green{\sf{To\:Find-}}$

Length of tangent.

$\underline\bold\red{\sf{Construction-}}$

Join OA such that ∠PAO = ∠OAQ = 30°

$\underline\bold\blue{\sf{Solution-}}$

We know that, tangents drawn from external point are equal.

AP = AQ _________(1)

We also know that, radius is always perpendicular to the tangent.

∠APO = AQO = 90°

Now, In right angled ∆APO,

$\sf \pink{TanØ = \dfrac{P}{B}}$

$\sf\implies \red{Tan 30° = \dfrac{OP}{AP}}$

$\sf\implies\green{\dfrac{1}{\sqrt3} = \dfrac{5}{AP} ( Tan30° = \dfrac{1}{\sqrt3})}$

$\sf \implies \blue{AP = 5√3}$

Also, AP = AQ ( from 1 )

Hence, AP = AQ = 5√3 cm.