A-cirlce-is-drawn-to-touch-the-sides-of-a-triangle-whose-sides-are-12cm-10cm-and-9cm-Find-the-radius-of-the-circle-

Question Number 16014 by chux last updated on 16/Jun/17

A cirlce is drawn to touch the

sides of a triangle whose sides are

12 cm, 10 cm, and 9 cm . Find the

radius of the circle .

Answered by RasheedSoomro last updated on 16/Jun/17

The circle which touches the sides

of a triangle is called in - circle and

its radius is called in - radius .

in - radius (r) is determined

by the formula below :

r = \frac{△}{s}

If a, b and c are the sides of the

triangle :

s = (a + b + c) / 2 s : semi - perimeter

△ = \sqrt{s (s - a) (s - b) (s - c)} △ : area of the triangle

We are given a = 12 cm, b = 10 cm, c = 9 cm

So s = (12 + 10 + 9) / 2 = 15.5

and △ = \sqrt{15.5 (15.5 - 12) (15.5 - 10) (15.5 - 9)}

= \sqrt{15.5 \times 3.5 \times 5.5 \times 6.5} \approx 44.04

Now the in - radius is

r = \frac{△}{s} = \frac{44.04}{15.5} = 2.84 cm

Commented by chux last updated on 16/Jun/17

thanks sir .

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