Trianglometry

Geometry Level 4

Triangle ABC has coordinates A, B and C equal to \( (5,3), (19,7)\) and \((17,25)\) respectively. By how much does the largest slope for any median of the triangle exceed the largest slope for any altitude of the triangle?

If the answer is in the form \(\frac ab\) for coprime positive integers \(a\) and \(b\), find the value of \(a-b\).

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