Let ABC be a 345 triangle with right angle C. Let D be a point on the hypotenuse. CD then partitions ABC into ACD and BCD.
Where is D located if ACD and BCD have congruent incircles?
Construction of point D for any right triangle.
If the triangle is isosceles, then D is the
midpoint of the hypotenuse; otherwise, label
the vertex opposite the shorter leg A and the
other vertex B.
Construct point E on line BC such that
CE = AC/2 and vertex C lies between B and E.
Label the midpoint of line segment BE as M.
Construct point F on side AC such that MF = ME.
The circle with center C and radius CF
intersects the hypotenuse AB at two points.
The point closest to vertex A is point D.

Posted by Bractals
on 20170107 12:15:30 