Question

If two tangents inclined at an angle 60° are drawn to a circle of radius 4 cm, then what is the
length of each tangent?​

Answer 1

Answer:

We know that AO and CO is the radius and with tangent radius make 90 degrees of angle.

So, angle ABO = angle BCO = 90 Degrees.

AO = OC = Radius of the circle.

AB = BC (Since tangents from one point on the same circle are equal)

First we consider triangle ABO,

The angle ABO is 30 degrees since the line from the center of the circle bisects the angle between two tangents from a point.

So we do,

tan30 = 13–√ = AOAB = 4ABAB = 43–√tan30 = 13 = AOAB = 4ABAB = 43

Hence AB =43–√43 cm.

So, the lengths of tangents = AB = BC = 43–√43cm.

Answer 2

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