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