Geometry question about a circle inscribed inside a triangle

Hello friends, I need help with a geometry question...

http://s8.postimage.org/z1zbxoe39/Semicircle_Triangle.jpg this is the triangle.

Here is what we know:

1) PQ is the diameter of the semicircle.

2) OE equals Radius

3) PQ is parallel to BC

4) AD is the altitude to BC

5) BC = 20, AD = 15

Now, the first part of the question asks us to prove that ABC and APQ have similarity. This I managed to do, so treat it as data.

The second part is to find the radius, and this is where I'm stuck...

Plz help me!

I

Re: Geometry question about a circle inscribed inside a triangle

Begin with $\displaystyle {PQ\over BC} = {AG\over AD}$

Re: Geometry question about a circle inscribed inside a triangle

Yes, I did that... And, according to the data, PQ is equal to 2R so: $\displaystyle \frac{2R}{20}= \frac{AG}{15}$

But AG is unknown, and I don't have the ratio, so I don't understand what I'm supposed to do here. I'm supposed to find something about the small triangle, a relation or something, but I just can't find it... I'm guessing there is a theorem about a semi circle inscribed inside a triangle or something, but I don't know it...

Re: Geometry question about a circle inscribed inside a triangle

Quote:

Originally Posted by

**chen888** Yes, I did that... And, according to the data, PQ is equal to 2R so: $\displaystyle \frac{2R}{20}= \frac{AG}{15}$

But AG is unknown, and I don't have the ratio, so I don't understand what I'm supposed to do here. I'm supposed to find something about the small triangle, a relation or something, but I just can't find it... I'm guessing there is a theorem about a semi circle inscribed inside a triangle or something, but I don't know it...

Note that $\displaystyle AG=15-R $. **WHY?**

Re: Geometry question about a circle inscribed inside a triangle

Now I got it! Thanks! But I don't understand, I thought it was illegal to use the same data twice when doing 2 equations/variables... ugh I sat like an hour on this thing now it's solved so simply I feel like I got kicked in the nuts...

Re: Geometry question about a circle inscribed inside a triangle

Quote:

Originally Posted by

**chen888** I thought it was illegal to use the same data twice when doing 2 equations/variables...

There is only one equation $\displaystyle {PQ\over BC} = {AG\over AD}$ and one unknown $\displaystyle R$. You can replace the length of the segments by any value depending on $\displaystyle R$.

Re: Geometry question about a circle inscribed inside a triangle

Ok I understand. Thanks very much for the help friends