Question

a circle is drawn through the vertices P, Q and R of a triangle PQR with PQ = 52 cm QR = 56 and PR = 6 cm. Find the diameter of the circle​

Answer 1

Answer:

72.46 cm

Step-by-step explanation:

A circle is drawn through the vertices P, Q and R of a triangle PQR.

with PQ = 52 cm, QR = 56 cm and PR = 6 cm.

If side of triangle a, b and c then circumradius R

$R=\dfrac{abc}{\sqrt{(a+b+c)(a+b-c)(a+c-b)(b+c-a)}}$

where, PQ=a=52 , QR=b=56, PQ=c=6

By substituting the value of a, b and c into formula.

$R=\dfrac{52\cdot 56\cdot 6}{\sqrt{(56+52+6)(52+56-6)(52+6-56)(56+6-52)}}$

$R\approx 36.23\text{ cm}$

As we know diameter is two times of radius.

D=2R

D=2 x 36.23

D = 72.46 cm

Hence, The diameter of circle is 72.46 cm