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find all possible values of AH/CH

Source: ItaMO 2005, P1

March 9, 2012
geometry proposedgeometry

Problem Statement

Let ABCABC be a right angled triangle with hypotenuse ACAC, and let HH be the foot of the altitude from BB to ACAC. Knowing that there is a right-angled triangle with side-lengths AB,BC,BHAB, BC, BH, determine all the possible values ​​of AHCH\frac{AH}{CH}
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