# Geometry question about a circle inscribed inside a triangle

• Jan 11th 2013, 09:37 AM
chen888
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.
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
• Jan 11th 2013, 10:54 AM
vincisonfire
Re: Geometry question about a circle inscribed inside a triangle
Begin with ${PQ\over BC} = {AG\over AD}$
• Jan 11th 2013, 11:25 AM
chen888
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: $\frac{2R}{20}= \frac{AG}{15}$
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...
• Jan 11th 2013, 12:07 PM
Plato
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: $\frac{2R}{20}= \frac{AG}{15}$
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 $AG=15-R$. WHY?
• Jan 11th 2013, 12:30 PM
chen888
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...
• Jan 11th 2013, 12:45 PM
vincisonfire
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 ${PQ\over BC} = {AG\over AD}$ and one unknown $R$. You can replace the length of the segments by any value depending on $R$.
• Jan 11th 2013, 01:32 PM
chen888
Re: Geometry question about a circle inscribed inside a triangle
Ok I understand. Thanks very much for the help friends