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

Asked on by lxsptter

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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).`

lxsptter | Student, Undergraduate | (Level 2) Valedictorian

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

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