# A triangle has corners at #(4 , 5 )#, #(1 ,3 )#, and #(5 ,3 )#. What is the radius of the triangle's inscribed circle?

The radius of the incircle is

The corners are

The length of the sides of the triangle are

The area of the triangle is

The radius of the incircle is

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

( r = \frac{2 \cdot \text{Area}}{a + b + c} )

Where ( r ) is the radius of the inscribed circle, ( \text{Area} ) is the area of the triangle, and ( a, b, ) and ( c ) are the lengths of the sides of the triangle.

You can calculate the area of the triangle using Heron's formula:

( \text{Area} = \sqrt{s \cdot (s - a) \cdot (s - b) \cdot (s - c)} )

Where ( s ) is the semi-perimeter of the triangle given by ( s = \frac{a + b + c}{2} ).

Once you have the area, you can plug it into the first formula along with the lengths of the sides to find the radius of the inscribed circle.

After calculating, the radius of the triangle's inscribed circle is approximately 0.6667 units.

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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 circle has a center at #(1 ,2 )# and passes through #(4 ,7 )#. What is the length of an arc covering #pi /4 # radians on the circle?
- The circumference of a circular field is 257.48 yards. What is the radius of the field? Use 3.14 for and do not round your answer.
- Two circles have the following equations #(x -1 )^2+(y -4 )^2= 36 # and #(x +5 )^2+(y -2 )^2= 49 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

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