in ,triangle pqr,angle Q=90,A CIRCLE WITH CENTRE O AND RADIUS 2 CM HAS BEEN INSCRIBED IN THE TRIANGLE.IF QR=6 CM ,FIND THE PERIMETER OF TRIANGLE PQR

Question

in ,triangle pqr,angle Q=90,A CIRCLE WITH CENTRE O AND RADIUS 2
CM HAS BEEN INSCRIBED IN THE TRIANGLE IF QR=6 CM ,FIND THE
PERIMETER OF TRIANGLE PQR

Aditi Rox · Answer

the perimeter is 24cm
as the radius is 2cm, QD = FO
hence QD=2cm

DR= 4cm (6-2)
as ER =DR (tangents from R)
ER=4cm
similarly FQ=2cm
let PF=PE=x cm

hence, perimeter of PQR = PQ+OR+PR
=(x+4) + 6 +(x+2)

x can be found by pythogoras theorm as PQR is a rt triangle
u'll get x as 6cm