Question

In figure, ABC is an isosceles triangle inscribed in a circle with centre O such that AB = AC = 13 cm and BC = 10 cm. Find the radius of the circle.

Answer 1

Given triangle ABC is isosceles with

AB = AC = 13 cm, BC = 10 cm

Step 1: Find the area of △ABC

`BD = DC = 10/2`

= 5 cm

Using Pythagoras in △ABD:

`AD = sqrt(13^2 - 5^2)`

`=sqrt(169-25)`

`=sqrt144`

= 12 cm

`Δ = 1/2xxBCxxAD`

`= 1/2xx10xx12`

= 60 cm²

Step 2: Use the circumradius formula

`R = (abc)/(4Δ)`

Here:

a = 13, b = 13, c = 10

`R = (13xx13xx10)/(4xx60)`

`= 1690/240`

`=169/24`

= 7.04 cm