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Coordinated Triangle?

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Author: Annie Fetter
Description: active problem Geometry, difficulty level 3. Triangle ABC has an area of 24 units^2. Point A is at (6,0); point B is at (10,0). Where can point C be? What if the triangle is isosceles?
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Problem page: http://mathforum.org/librarypow/puzzles/index2.ehtml?puzzle=603
Solution page: Problem #603

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