Question

In triangle, Ab =20cm , Bc=21cm,Ac =29cm. Find the radius of the circle touching all the sides of triangle ABC

Answer 1

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Answer 2

Answer:

6 units

Step-by-step explanation:

Given,

The sides of the triangle ABC,

AB =20cm , BC=21cm, AC =29cm,

Thus, the semi perimeter of the triangle ABC,

$s=\frac{1}{2}(AB+BC + AC)=\frac{1}{2}(20+21+29)=\frac{1}{2}(70)=35$

So, by the heron's formula,

The area of the triangle,

$A=\sqrt{s(s-AB)(s-BC)(s-AC)}$

$=\sqrt{35(35-20)(35-21)(35-29)}$

$=\sqrt{35(15)(14)(6)}$

= 210 square unit,

Hence, the radius of the circle touching all the sides of triangle ABC,

$R=\frac{A}{s}=\frac{210}{35}=6\text{ unit}$