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# Geometry

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What is the radius of the circle inscribed in triangle ABC\$ if AB = 15, AC = 41, and BC = \(42\)?

Apr 14, 2022

#1
+2

The Radius of a circle inscribed in a triangle can be found using the formula Area of triangle/semi perimeter of the triangle:

We can find the semi perimeter by adding all the known sides and dividing by 2.

That would be (15+41+42)/2 = 98/2 = 49

We can find the area of the triangle using the heron's formula:

sqrt(49(49-15)(49-41)(49-42))

= 28*sqrt(119) = approx 305.44393

Substituting that in the Area of triangle/semi perimeter of the triangle formula:

28*sqrt(119)/49

= (4sqrt(17))/sqrt(7) or approx.  6.23354 units

If you want, rationalise the radical. Its up to you -Vinculum   Apr 14, 2022
edited by Vinculum  Apr 14, 2022

#1
+2

The Radius of a circle inscribed in a triangle can be found using the formula Area of triangle/semi perimeter of the triangle:

We can find the semi perimeter by adding all the known sides and dividing by 2.

That would be (15+41+42)/2 = 98/2 = 49

We can find the area of the triangle using the heron's formula:

sqrt(49(49-15)(49-41)(49-42))

= 28*sqrt(119) = approx 305.44393

Substituting that in the Area of triangle/semi perimeter of the triangle formula:

28*sqrt(119)/49

= (4sqrt(17))/sqrt(7) or approx.  6.23354 units

If you want, rationalise the radical. Its up to you -Vinculum   Vinculum Apr 14, 2022
edited by Vinculum  Apr 14, 2022
#2
+1

When it is rationalised, it is (4sqrt(119))/7

ch1ck3n  Apr 14, 2022