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| Math Central | Quandaries & Queries |
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Question from Patrick: I'm trying to find a quick calculation to find the center of the circle that will touch the 3 points of an isosceles triangle.<br /> |
Hi Patrick,
In my diagram the center $C$ of the circle is between the top point $P$ and the middle $M$ of the base.
Let the radius of the circle be $r$ and then $|PC| = |CR| = r.$ If $h$ is the height of the triangle then $|CM| = h-r.$ Let the distance from $M$ to $R$ be $b,$ which is half the length of the base of the triangle. Triangle $PMR$ is a right triangle. Use Pythagoras theorem for this triangle and solve for $r.$
Apply a similar argument to find $r$ if $M$ is between $P$ and $C.$
Penny
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