Question

AB is a tangent to the circle centred at 0, as shown below. Given that AB and BC are the same length, work out the size of angle x. Justify your answer.

Answer 1

The calculated size of the angle x is 45 degrees

How to determine the size of the angle x

From the question, we have the following parameters that can be used in our computation:

The circle O

Since AB is a tangent to the circle, then

∠ABC = 90 degrees i.e. angle between a circle and the radius

Also, we have that

AB and BC are of the same length

This means that Δ is an isosceles triangle

So, we have

x + x + 90 = 180 --- by the sum of angles in a triangle

This gives

2x = 90

Evaluate

x = 45

Hence, the size of the angle x is 45 degrees