Hello, lego_lax!

If no one is responding, it's that we didn't understand the description.

After a number of incorrect sketches, I finally caught on.

I have inscribed in a circle with .

The height relative to BC is equal to the radius.

On the line BA take the segment AD equal to AC.

Prove that the line DC is tangent to the circle. Code:

D
*
/
/
/
/
A/
* o *
* / \* *
* / \ * *
* / \ * *
/ r\ * *
* / \ o C
* / o *
* / * E *
/ *
B o *
* *
* *
* * *

We have inscribed triangle , with

Extend to so that

Prove that is tangent to the circle.

Now I can give it a try . . .