Question

A pair of tangents to a circle which is inclined to each other at an angle of 60 degree are drawn at ends of two radii. The angle between these radii must be :

Answer 1

The angle between these radii must be 120º.

Explanation:

According to Euclidean Geometry, two tangents to a circle are symmetrical to each other and the axis of symmetry passes through the center of the circle and, hence, each tangent is perpendicular to a respective radius. We represent the statement in the diagram included below.

Then, we calculate the angle of the radius with respect to the axis of symmetry by knowing the fact that sum of internal angles within triangle equals 180º. That is to say:

`\theta = 180^(\circ)-90^(\circ)-30^(\circ)`

`\theta = 60^(\circ)`

And the angle between these two radii is twice the result.

`\theta' = 2\cdot \theta`

`\theta' = 120^(\circ)`

The angle between these radii must be 120º.