In Δ ABC, AB = 12 cm, BC = 16 cm and AC = 20 cm. A circle is inscribed inside the triangle. What is the radius (in cm) of the circle? 

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Answer (Detailed Solution Below)

Option 2 : 4
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Detailed Solution

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Given:

In Δ ABC, AB = 12 cm, BC = 16 cm, AC = 20 cm

Formula used:

Area of the triangle (Δ) = \(\sqrt{s(s-a)(s-b)(s-c)}\)

Where s = semi-perimeter = \(\frac{a+b+c}{2}\)

Radius (r) of the inscribed circle = \(\frac{\Delta}{s}\)

Calculations:

5-5-2025 IMG-1083 Prakhar -4

a = 12 cm, b = 16 cm, c = 20 cm

s = \(\frac{12+16+20}{2}\) = 24 cm

Area (Δ) = \(\sqrt{24(24-12)(24-16)(24-20)}\)

⇒ Area (Δ) = \(\sqrt{24×12×8×4}\)

⇒ Area (Δ) = \(\sqrt{9216}\)

⇒ Area (Δ) = 96 cm2

Radius (r) = \(\frac{96}{24}\)

⇒ Radius (r) = 4 cm

∴ The correct answer is option (2).

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