# Math Help - circle

1. ## circle

Sorry >__<

I need help on this question

There is a circle inscribed in a triangle.

so if AB=12, BC=16, and AC= 20, <B=90...then what is the radius of the inscribed circle?

I dunno how to draw a picture here.......but the diagram should be a scalene triangle with a circle inscribed inside it.

2. I believe the radius is the following:

$r = \frac{\sqrt{k(k-a)(k-b)(k-c)}}{k}$ (Herons Formula) where $k = \frac{1}{2}(a+b+c)$.

So $k = \frac{1}{2}(20 + 16 + 12) = 24$.

And $r = \frac{\sqrt{24(24-20)(24-16)(24-12)}}{24} = 4$

3. Use Poncelet's Theorem

$12+16=20+2r\implies{r}=4$

4. Hello, charrie berri!

There is a circle inscribed in triangle $ABC$.

If $AB=12,\;BC=16,\;AC= 20,\;\angle B = 90^o$
. . what is the radius of the inscribed circle?
The radius $r$ of the inscribed circle can be found with: . $A \;=\;\frac{1}{2}pr$
. . where: . $\begin{array}{ccc} p & = & \text{perimeter} \\ r & = &\text{radius} \\ A & = & \text{area} \end{array}$

The perimeter is: . $p \:=\:12 + 16 + 20 \:=\:48$

The area is: . $A \:=\:\frac{1}{2}(12)(16) \:=\:96$ .
. . . It's a right triangle!

So we have: . $96 \:=\:\frac{1}{2}(48)r\quad\Rightarrow\quad\boxed{r \,=\,4}$

5. THANK YOU!!! I REALLY APPRECIATE IT.

And I need help on one last question........

In Circle O, <OAB=24 and <OCB= 60. What is the measure of <ABC.....