Radius of a circle that intersects two points on a right triangle.

[dgoldman86]

I'm trying to figure out the radius of a circle that intersects two points on a right triangle. One side of the triangle is tangent to the circle and the other intersects it. I have attached an image that helps further explain what I'm talking about. Knowing what I have listed in the image is there anyway to determine the radius of that circle?

Thanks.

 

[henry_m]

Try using coordinate geometry. Let the point where the triangle is tangent to the circle be the origin, and let that side of the circle run parallel to the x-axis. What's the equation of the circle? What are the coordinates of the point where the triangle touches the circle?

 

[jorgealnino]

How about this

Call the vertex of your right triangle (c_1,r,c2) with c_1 tangent to the circle and r the vertex at the right angle. Let o be the center of your circle.
Now construct the square (o,c_1,r,s).
Observe that c_2 is on the square side (r,q) and use pythagoras.