Question

The perimeter of right trianglePQR is 36 cm. A circle inscribed in this triangle touches hypotenuse at C such that PC:CR = 2:3. then sides (in cm) of triangle PQR are.​

Answer 1

Answer.

AB+BC−AC

As we know, △ABC is a right angle triangle,

so, area of △ABC =

2

1

AB×BC

Also we can see in the figure that, area of △ABC = area of △AOB + area of △BOC + area of △AOC

so, area of △ABC = =

2

1

r×AB +

2

1

r×BC +

2

1

r×CA

∴, area of △ABC = =

2

1

r×(AB+BC+CA)

Equating both the equations, we get

AB×BC = r×(AB+BC+CA)

2r=

AB+BC+CA

2AB×BC

2r=

AB+BC+CA

(AB+BC)

2

−(AB

2

+BC

2

)

Also, we know by pythagoras theorem, AC

2

= AB

2

+ BC

2

2r=

AB+BC+AC

(AB+BC)

2

−AC

2

2r=

AB+BC+AC

(AB+BC−AC)×(AB+BC+AC)

∴2r= AB+BC−AC