Question

A circle is inscribed inside ΔPQR. The measure of sides PQ, QR and PR of Δ PQR is 30 cm, 40 cm and 50 cm respectively. Find the measure of in-radius of ΔPQR.

1. 8 cm
2. 10 cm
3. 5 cm 
4. 14 cm

Answer 1

Correct Answer - Option 2 : 10 cm

Given:

In ΔPQR,

PQ = 30 cm, QR = 40 cm and PR = 50 cm

Concepts used:

Area of right-angled triangle = ½ × base × height

Area of triangle circumscribing a circle = ½ × in-radius × (sum of all sides of triangle)

Calculation:

As (30, 40, 50) forms a Pythagorean triplet,

⇒ PR² = PQ² + QR²

⇒ ∠Q is the right-angle and ΔPQR is right-angled triangle.

Area of ΔPQR = ½ × 30 × 40 cm² =  cm²

Let in-radius of ΔPQR be r.

Area of triangle circumscribing a circle = ½ × in-radius × (sum of all sides of triangle)

⇒ 600 cm² = ½ × r × (30 + 40 + 50) cm

⇒ 600 cm² = 120r/2 cm

⇒ r = 600 × 2/120 cm

⇒ r = 10 cm

∴ Length of in-radius of ΔPQR is equal to 10 cm.