Right Triangles and Circles

Given distinct points A and B, prove {E: IAEI² + IBEI² = IABI²} is a circle.
Determine the center and radius.

If we have a segment AB and a ray AC we can create a line perpendicular to AC. The point where AB and BD meet is E. So triangle ABE is a right triangle.

To see that all possible points of E form a circle, drag point C around.

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The center of the circle is the midpoint of segment AB and the radius is half the length of segment AB, since AB is the diameter of the circle.

Teresa Munninghoff, Created with GeoGebra