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 Congruent Incircles (Posted on 2017-01-01)
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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 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, labelthe vertex opposite the shorter leg A and theother 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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