Question

ABC is a right angled triangle, right angled at B with AB = 3 cm and BC = 4 cm. A circle which touches all the sides of the triangle is inscribed in the triangle. Calculate the radius of the circle.

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Answer 1

Given that AB = 3 cm, BC = 4 cm

Applying Pythagoras theorem to $△$ABC we get

${AC}^2$ = ${AB}^2$ + ${BC}^2$

${AC}^2$ = $3^2$ + $4^2$

${AC}^2$ = 25

AC = 5 cm

Let AQ = AP = l, BQ = BR = n, CR = CP = m

l+n=3 ……(i)

n+m=4 $\Rightarrow$ n=4-m

Substituting in (i)

l+4-m=3

l-m=-1 …..(ii)

l+m=5 ….(iii)

Adding (ii) and (iii)

2l=4

l=2

n=1

But n=$x$ i.e. the radius of the circle

Therefore the radius of the circle is 1 cm.