Question

if you draw a pair of tangents of a circle with centre o and radius r
from p such that op =2r,then find the angle between the two tangents

Answer 1

sinQ=perpendicular/hypotenuse
sinQ=r/2r1101019022412170113
sinQ=1/2
but 1/2=Sin30°
so,Q=30
thus angle between tangents= 2Q
= 2x30°=60° and

if you did not understand you may message
I will try to make you understood on my notebook

Answer 2

Given,

A circle with centre 'o' and radius, r.

Two tangents are drawn from point p.

op = 2r

To find,

The angle between two tangents.

Solution,

The angle between two tangents will be 60°.

According to the question,

A circle with centre 'o' and radius, r.

Two tangents are drawn from point p.

op = 2r

We know that the tangent from a point makes a right angle with the radius.

Now, let's take the point where the two tangents touch the circumference to be a and b.

So, ∆ oap is a right-angled triangle.

op will divide the angle between the two tangents into halves.

Now, using the trigonometric function,

Sin p/2 = oa/op

Sin p/2 = r/2r

sin p/2 = 1/2

We know that the value of sin 30° is 1/2.

sin p/2 = sin 30°

p/2 = 30°

p = (2×30)°

p = 60°

Hence, the angle between two tangents is 60°.