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


by dgoldman86
Tags: circle, intersects, points, radius, triangle
dgoldman86
dgoldman86 is offline
#1
May18-11, 09:06 PM
P: 3
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 Thumbnails
Circle.JPG  
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henry_m
henry_m is offline
#2
May19-11, 05:55 AM
P: 160
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
jorgealnino is offline
#3
May22-11, 03:37 AM
P: 3
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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