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

  • Thread starter dgoldman86
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  • #1
dgoldman86
3
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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.
 

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  • Circle.JPG
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Answers and Replies

  • #2
henry_m
160
2
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?
 
  • #3
jorgealnino
3
0
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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