# A triangle has corners at #(3 , 4 )#, #(6 ,7 )#, and #(5 ,8 )#. What is the radius of the triangle's inscribed circle?

By signing up, you agree to our Terms of Service and Privacy Policy

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

[ r = \frac{{\text{Area of the Triangle}}}{{\text{Semi-perimeter of the Triangle}}} ]

First, calculate 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, find the semi-perimeter (s) of the triangle:

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

Next, calculate the area (A) of the triangle using Heron's formula:

[ A = \sqrt{s(s - \text{Side 1})(s - \text{Side 2})(s - \text{Side 3})} ]

Finally, plug the values of A and s into the formula for the radius (r) to find the radius of the inscribed circle.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- AB is diameter whose center is O of a circle. If AC is 3 cm and BC is 4 cm, then find AB?
- A circle has a chord that goes from #( 3 pi)/4 # to #(5 pi) / 4 # radians on the circle. If the area of the circle is #144 pi #, what is the length of the chord?
- A circle has a center at #(7 ,9 )# and passes through #(4 ,3 )#. What is the length of an arc covering #pi /4 # radians on the circle?
- A triangle has corners at #(3 , 4 )#, #(6 ,3 )#, and #(5 ,8 )#. What is the radius of the triangle's inscribed circle?
- A circle has a chord that goes from #( 3 pi)/2 # to #(7 pi) / 4 # radians on the circle. If the area of the circle is #99 pi #, what is the length of the chord?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7