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

  1. 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.
     

    Attached Files:

  2. jcsd
  3. 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?
     
  4. 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.
     
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