Question

$△$ABC is a right- angled triangle with AB = 12 cm and AC = 13 cm. A circle with center O has been inscribed inside the triangle. Calculate the radius of the inscribed circle.

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Answer 1

Given that AB = 12 cm, AC = 13 cm

Applying Pythagoras theorem to $△$ABC

${BC}^2$ = ${AC}^2$ – ${AB}^2$

${BC}^2$ = ${13}^2$ - ${12}^2$

BC = 5 cm

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

l+n=12 …..(i)

n+m=5$\Rightarrow$ n=5-m

Equation (i) becomes l+5-m=12

l-m=7 …..(ii)

l+m=13 …..(iii)

Adding (ii) and (iii)

2l=20

l=10

n=2

But n= radius of the circle

Therefore the radius of the circle is 2 cm.