A triangle has sides with lengths of 8, 7, and 6. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-01-25T02:32:44

If $a, b and c$ $a, b and c$ are the three sides of a triangle then the radius of its in center is given by

$R=Delta/s$

Where $R$ is the radius $Delta$ is the are of the triangle and $s$ is the semi perimeter of the triangle.

The area $Delta$ of a triangle is given by

$Delta=sqrt(s(s-a)(s-b)(s-c)$

And the semi perimeter $s$ of a triangle is given by
$s=(a+b+c)/2$

Here let $a=8, b=7 and c=6$

$implies s=(8+7+6)/2=21/2=10.5$

$implies s=10.5$

$implies s-a=10.5-8=2.5, s-b=10.5-7=3.5 and s-c=10.5-6=4.5$

$implies s-a=2.5, s-b=3.5 and s-c=4.5$

$implies Delta=sqrt(10.5*2.5*3.5*4.5)=sqrt413.4375=20.333$

$implies R=20.333/10.5=1.9364$ units

Hence, the radius of inscribed circle of the triangle is $1.9364$ units long.