# A triangle has corners at #(3 , 5 )#, #(4 ,2 )#, and #(8 ,4 )#. What is the radius of the triangle's inscribed circle?

Radius of triangle's inscribed circle is

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To find the radius of the inscribed circle in a triangle, you can use the formula:

[ r = \frac{2A}{P} ]

where ( A ) is the area of the triangle and ( P ) is the perimeter of the triangle.

First, calculate the lengths of the sides of the triangle using the given coordinates:

Side 1: [ \sqrt{(4-3)^2 + (2-5)^2} ]

Side 2: [ \sqrt{(8-4)^2 + (4-2)^2} ]

Side 3: [ \sqrt{(8-3)^2 + (4-5)^2} ]

Then, use Heron's formula to find the area of the triangle:

[ A = \sqrt{s(s-a)(s-b)(s-c)} ]

where ( s ) is the semi-perimeter of the triangle, and ( a, b, c ) are the lengths of the sides.

Finally, calculate the radius of the inscribed circle using the formula given above.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- A triangle has corners at #(6 , 6 )#, #(4 ,4 )#, and #(1 ,2 )#. What is the radius of the triangle's inscribed circle?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #9 #. What is the area of the triangle's incircle?

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