A triangle has corners at (3 , 2 ), (6 ,7 ), and (2 ,4 ). What is the radius of the triangle's inscribed circle?

1 Answer
Harish Chandra Rajpoot
Jul 11, 2018

0.842

Explanation:

The area \Delta of triangle with vertices (x_1, y_1)\equiv(3, 2), (x_2, y_2)\equiv(6, 7) & (x_3, y_3)\equiv(2, 4) is given by following formula

\Delta=1/2|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|

=1/2|3(7-4)+6(4-2)+2(2-7)|

=5.5

Now, the lengths of all three sides say a, b & c of given triangle are computed by using distance formula as follows

a=\sqrt{(3-6)^2+(2-7)^2}=\sqrt34

b=\sqrt{(6-2)^2+(7-4)^2}=5

c=\sqrt{(3-2)^2+(2-4)^2}=\sqrt5

hence, the semi-perimeter s of given triangle is computed as follows

s=\frac{a+b+c}{2}

=\frac{\sqrt34+5+\sqrt5}{2}=6.533

hence, the radius of inscribed circle is given as

\frac{\Delta}{s}

=\frac{5.5}{6.533}

=0.842

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