# A triangle has corners at #(5 , 2 )#, #(4 ,7 )#, and #(5 ,6 )#. What is the radius of the triangle's inscribed circle?

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To find the radius of the triangle's inscribed circle, you can use the formula:

[ r = \frac{2 \times \text{Area of the Triangle}}{\text{Perimeter of the Triangle}} ]

The coordinates of the triangle's vertices are given as ( (5, 2) ), ( (4, 7) ), and ( (5, 6) ). You can calculate the lengths of the sides of the triangle using the distance formula between two points. Then, you can find the semi-perimeter ( s ) of the triangle.

After that, you can use Heron's formula to find the area of the triangle. Once you have the area and the perimeter, you can use the formula mentioned earlier to find the radius of the inscribed circle.

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

[ r = \frac{\text{Area of the triangle}}{\text{Semiperimeter of the triangle}} ]

First, we need to find the lengths of the sides of the triangle using the distance formula:

[ \text{Side 1} = \sqrt{(4-5)^2 + (7-2)^2} ] [ \text{Side 2} = \sqrt{(5-5)^2 + (6-7)^2} ] [ \text{Side 3} = \sqrt{(5-4)^2 + (6-2)^2} ]

Then, we'll find the semiperimeter of the triangle, which is half the sum of its sides:

[ \text{Semiperimeter} = \frac{\text{Side 1} + \text{Side 2} + \text{Side 3}}{2} ]

Next, we'll find the area of the triangle using Heron's formula:

[ \text{Area} = \sqrt{\text{Semiperimeter} \times (\text{Semiperimeter} - \text{Side 1}) \times (\text{Semiperimeter} - \text{Side 2}) \times (\text{Semiperimeter} - \text{Side 3})} ]

Once we have the area of the triangle and the semiperimeter, we can calculate the radius of the inscribed circle using the formula mentioned earlier.

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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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