Question

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of ${60}^{\circ }$

Answer 1

Hint:
1. Tangent to a circle
A tangent to a circle is a straight line, in the plane of the circle, which touches the circle at only one point. The point is called the point of tangency of the point of contact.
2. Tangent to a circle theorem

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

3. Two tangent theorem
When two segments are drawn tangent to a circle from the same point outside the circle, the segments are equal in length.
 $\mathrm{\angle }BOA+\mathrm{\angle }BPA={180}^{\circ }$

Complete step-by-step answer:
First we will draw a rough sketch of the given problem.
Rough sketch

Now we will construct the above given tangents by using following steps
Steps of construction
1. Draw circle with centre O and radius $OA=5cm$
2. Make another point B on circle such that $\mathrm{\angle }AOB={120}^{\circ }$ supplementary to the angle between the tangents to be constructed is ${60}^{\circ }$
 $\therefore \mathrm{\angle }AOB=180-{60}^{\circ }={120}^{\circ }$
3. Construct angles of ${90}^{\circ }$ at A and B and extend the lines so as to intersect at point P.
4. Thus, AP and BP are required tangents

Note: In every question related to construction we should make a rough figure. It will make our construction easier. Also see the quadrilateral AOBP and observe all angles their sum is equal to 60 degree.