Question
Download Solution PDFIn 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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:
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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