The circle has radius 5 cm. Two tangents are drawn from an external point, with an angle of 60° between them.
Let O be the center of the circle, P be the external point where the tangents meet, and A and B be the points where the tangents touch the circle.
The line OP bisects the angle between the two tangents.
Since angle APB = 60°:
Angle OPA = 260°
Angle OPA = 30°
Consider triangle OAP:
The tangent is perpendicular to the radius at the point of contact, so angle OAP = 90°.
OA = 5 cm (radius)
PA = length of tangent (to find)
In right triangle OAP:
tan(30°)=PAOA
31=PA5
PA=53 cm
Therefore, the length of each tangent is 53 cm.