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Congruent Incircles (Posted on 2017-01-01) Difficulty: 4 of 5
Let ABC be a 3-4-5 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?

No Solution Yet Submitted by Brian Smith    
Rating: 5.0000 (1 votes)

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Some Thoughts Construction of point D for any right triangle Comment 6 of 6 |

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 2017-01-07 12:15:30
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