Simply Geometry......

Geometry Level 1

A circle is inscribed in a triangle of sides 3, 4 and 5 cm. Find it's radius


The answer is 1.

Vaibhav Kandwal by Vaibhav Kandwal , 21, India

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2 solutions

Vaibhav Kandwal
Jan 18, 2015

Using the formula, R = A r e a o f t r i a n g l e S e m i p e r i m e t e r R = \dfrac{Area of triangle}{Semiperimeter} ,

We get, Area of triangle as 6 c m 2 6cm^2 and Semi-Perimeter as 6 c m 6cm

R= 6 6 = 1 \dfrac{6}{6}=\boxed{1}

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r = 2 A P r=\dfrac{2A}{P} where A = a r e a , P = p e r i m e t e r A=area,P=perimeter

r = 2 ( 1 2 ) ( 3 ) ( 4 ) 3 + 4 + 5 = 12 12 = r=\dfrac{2\left(\dfrac{1}{2}\right)(3)(4)}{3+4+5}=\dfrac{12}{12}= 1 \color{#D61F06}\boxed{1}

Note that the triangle is a right triangle.

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