Question

In a triangle PQR, PQ = 12 cm and QR = 4√3 If the measure of PRQ = 60° then what is the ratio of the inradius to the circumradius of the triangle PQR?​

Answer 1

Step-by-step explanation:

By Pythagoras' theorem,

PR

2

=PQ

2

+QR

2

PR

2

=24

2

+7

2

=576+49=625

∴PR=25 cm

Let the inradius of △PQR be x cm.

□OAQC is a square. Hence QA=x cm and AR=(7−x) cm

RA and RB act as tangents to the incircle from point R, hence their lengths are equal. ∴RB=AR=(7−x) cm.

Similarly, PB=PC=(24−x) cm

PR=PB+RB

⇒25=(24−x)+(7−x)

⇒25=31−2x

⇒x=3 cm