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  4. The number of triangles which are obtuse and which have the points (8,9),(8,16) and (20,25) as the feet of perpendiculars drawn from the vertices on the opposite sides is

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Q. The number of triangles which are obtuse and which have the points $(8,9),(8,16)$ and $(20,25)$ as the feet of perpendiculars drawn from the vertices on the opposite sides is

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Solution:

There exist exactly four triangles $A B C, A P C, A P B$ and $B P C$ satisfying the given conditions of which three triangles will be obtuse angle.
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