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# 2 tangents making an angle of 120 degrees with each other, are drawn to a circle of radius 6 cm, then the length of each tangent is equal to?

10 years ago

dear student,draw a circle of radius 6cm.draw an angle aob of 120degree.at A and B,draw an angle 90degree wich meets at C.then ,AC and BC are the  required tangents which are inclined to each other at an angle of 60 degree.

10 years ago

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