A triangle has corners at #(3 , 4 )#, #(8 ,2 )#, and #(1 ,8 )#. What is the radius of the triangle's inscribed circle?

Answer 1

The radius of inscribed circle #r=0.8387131004" "#unit

Let us label the points #A(3, 4)#, #B(8, 2)#, #C(1, 8)# Solve for the distances #a=BC# and #b=AC# and #c=AB#
The radius of the inscribed circle #r# formula
#r=sqrt(((s-a)(s-b)(s-c))/s)#

Solve for the values of s, a, b, and c first

#a=sqrt((x_b-x_c)^2+(y_b-y_c)^2)# #a=sqrt((8-1)^2+(2-8)^2)# #a=sqrt85#
#b=sqrt((x_a-x_c)^2+(y_a-y_c)^2)# #b=sqrt((3-1)^2+(4-8)^2)# #b=sqrt20#
#c=sqrt((x_a-x_b)^2+(y_a-y_b)^2)# #c=sqrt((3-8)^2+(4-2)^2)# #c=sqrt(29)#
Half the Perimeter of the triangle #s#
#s=(a+b+c)/2=(sqrt85+sqrt20+sqrt29)/2#
Compute #r#
#r=# #sqrt((((sqrt85+sqrt20+sqrt29)/2-a)((sqrt85+sqrt20+sqrt29)/2-b)((sqrt85+sqrt20+sqrt29)/2-c))/[0.5*(sqrt85+sqrt20+sqrt29)])#
#r=0.8387131004#

God bless....I hope the explanation is useful.

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Answer 2

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

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

First, calculate the semiperimeter ( s ) of the triangle using the formula:

[ s = \frac{{\text{sum of all three sides}}}{{2}} ]

Then, find the area ( A ) of the triangle using Heron's formula:

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

where ( a ), ( b ), and ( c ) are the lengths of the sides of the triangle.

Once you have both the semiperimeter and the area, you can find the radius ( r ) using the first formula mentioned.

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Answer from HIX Tutor

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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