Steps of construction:

1) Draw a line BC = 4 cm

2) Taking B as center, draw an arc of radius 5 cm and then taking C as center, draw an arc of 6 cm which intersects previous arc at A.

ABC is the required triangle.

3) Draw the angle bisector of ∠ABC and ∠ACB, which intersect each other at O.

4) Draw OP ⊥ BC, and taking O as center, draw a circle with radius as OP.

Calculation of radius:

We know, radius of incircle

Where, A = area of triangle

And s = semi-perimeter of triangle

Also, We know, area of triangle = √(s(s - a)(s - b)(s - c))

Where, a, b and c are sides and s is the semi-perimeter calculated as

∴

⇒ area = √(7.5(7.5 - 4)(7.5 - 5)(7.5-6)

= √(7.5 × 3.5 × 2.5 × 1.5 )