A triangle has corners at #(2 ,3 )#, #(1 ,9 )#, and #(6 ,8 )#. What is the radius of the triangle's inscribed circle?
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To find the radius of the triangle's inscribed circle, we can use the formula:
[ r = \frac{A}{s} ]
Where ( A ) is the area of the triangle and ( s ) is the semi-perimeter of the triangle.
- First, we need to find the lengths of the sides of the triangle using the distance formula:
[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]
- Then, calculate the semi-perimeter ( s ) using the formula:
[ s = \frac{a + b + c}{2} ]
Where ( a ), ( b ), and ( c ) are the lengths of the sides.
- Next, calculate the area ( A ) of the triangle using Heron's formula:
[ A = \sqrt{s(s - a)(s - b)(s - c)} ]
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Finally, plug the values of ( A ) and ( s ) into the formula for the radius ( r ).
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The radius ( r ) is the desired value.
Let's proceed with these calculations.
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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.
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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