Question

A circle is drawn through the vertices P, Q and Rof a triangle PQR with PQ = 52 cm, QR = 56 cm and PR = 60 cm as shown in the given
figure. Find the diameter of the circle.​

Answer 1

Answer:

The diameter of the circle is 48.64 cm

Explanation:

In the question length of PQ= 52cm, QR= 56cm and PR=60cm is given.

If side of triangle is a, b and c then circum-radius $R=\frac{a b c}{\sqrt{(a+b+c)(a+b-c)(a+c-b)(b+c-a)}}$

Length of circumradius PQ=a= 52, QR=b= 56 and PR=c= 60

$\begin{array}{l}{R=\frac{52 \times 56 \times 60}{\sqrt{(52+56+60)(52+56-60)(52+60-56)(56+60-52)}}} \\ {R=\frac{174720}{\sqrt{516096}}} \\ {R=\frac{174720}{718.39}}\end{array}$

R= 24.32 (approx)

D = 2R

D= 2 X 24.32 = 48.64 cm of diameter.