# What is the area of the triangle that just fits around a circle of radius 12.

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### 2 Answers

You need to remember that the triangle is tangent to circle and the tangency points split the sides of triangle in the lengths a and b, b and c, c and a.

You need to use the formula that expresses the radius of incircle in terms of these lengths such that:

`r = sqrt ((abc)/(a+b+c))`

Substituting 12 for r yields:

`12 = sqrt ((abc)/(a+b+c)) =gt 144 = ((abc)/(a+b+c)) =gt abc = 144(a+b+c)`

You need to use the formula that expresses the of area of triangle in terms of lengths a,b,c such that:

`A = sqrt(abc(a+b+c))`

You need to substitute `144(a+b+c)` for abc such that:

`A = sqrt(144(a+b+c)(a+b+c)) `

`A = 12(a+b+c)`

You need to remember that a+b+c expresses the half perimeter of triangle.

**Hence, evaluating the area of triangle that fits around circle of radius 12 yields that area is 12 times half of perimeter of triangle such that: `A = 12(a+b+c).` **

But the area of a triangle using Heron formula is sqrt(s(s - a)(s - b)(s - c)) where s = (a + b+c)/2