Take a right triangle and let its altitude from the right angle divide the hypotenuse into parts of lengths

aandb. Interpret the comparison of the lengths of the altitude and the median from the 90 degree vertex of a right triangle having hypotenuse of lengtha+b.Clearly, the length of the median is always greater than or equal to the length of the altitude. Express the lengths of median and the altitude in terms of

aandb.

Conclusion? _______________________________

Hints/Solution:

Extensions/Variations:

Consider the triangles inscribed in a semicircle with one side formed by the diameter.

Reference:

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