Question 90
On the side $AB$ of the rectangle $ABCD$ are taken the points $S$ and $T$ so that $AS = ST = TB$. Denote $M, N$ and $P$ the orthogonal projections of $A, S$ and $T$ onto the straight lines $DS, DT$ respectively $DB$. Prove that the points $M, N$ and $P$ are collinear if and only if $15AD^2 = 2AB^2$.
Gabriel Popa
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Gabriel Popa
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