Two tangents making an angle of 120 with each other are drawn to a circle of radius, find the length of each tangent.

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Solution

let point of intersection is P & center of circle is O ...

let one of the tangent touches the circle at R then

POR is a right angled triangle with OPR = 60o , POR = 90o & POR = 30o ...

now let three sides of this triangle are a,b,c then

a/sinA = b/sinB = c/sinC by using this identity we get

L/sin30 = R/sin60

L = R/root3

L is length of tangent

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