Question

PQR is right angled triangle with QR=12cm and PQ=5cm . A circle with center o is inscribed in triangle PQR. find the radius of the circle.

Answer 1

Answer in in image given above.....

Answer 2

The radius of the circle is 2 cm

Solution:  

From the below diagram:-

RA + AO = 12     ______ (1)

RC + CP = 13 _______ (2)          

OB + BP = 5 _______ (3)

Now from the above figure  

Side AO = Side OB = Radius of the circle

Side RA = Side RC  

Line BP = Line CP

Rewriting these three equations we get

RA + AO = 12 _______ (4)

RA + BP = 13 _______ (5)

AO + BP = 5 _______(6)

(4) – (6) + (5)

RA – BP = 7

RA + BP = 13

2 RA = 20

RA = 10

From equation 4, AO = 12 – 10 = 2 cm

Since AO is equal to radius of the inscribed circle, radius = 2 cm.