Question

PQR is an isosceles triangle inscribed in a circle with
centre O such that PQ = PR = 13 cm and QR = 10 cm. Find
the radius of the circle.​

Answer 1

Given:

PQ = PR = 13 cm and QR = 10 cm

To find:

radius of the circle.

Solution:

1) The triangle inscribed in the circle which means that this is the case of the circumcircle.

2) there is the direct formula to find the radius of the circumcircle which is

a×b×c/4× area of ∆

3) In ΔPMR

PM² + MR² = PR² (by Pythagoras theorem)

PM² + 5²   = 13²

PM² + 25 = 169

PM² = 144

PM  = √144 = 12 cm.

4)Radius of circumcircle = a×b×c / 4×ar of Δ

Area of ΔPQR = 1/2 B H

                       = 1/2 ×10 ×12

                        = 60 cm²

Radius = 13×13×10 / 4×60

           = 7.014 cm

Radius of the circle is 7.014 cm.