The following triangle has an area $S$, and the sides $AO$ and $BO$ have the length $a$ and $b$, respectively. There is a fixed point $X$ at $(x,y)$. A point $C$ is put on the line segment $OA$, and the point $D$ is put on the intersection between the line segment $OB$ and the line $CX$. When does the area of the triangle $DCO$ have the smallest value? I think it is either when $DX=XC$, when $D$ is at $B$, or when $C$ is at $A$. Yet, if I try to prove this, calculation becomes so complicated.
Best Answer
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Hint:
Solution. With increasing detail (move mouse/cursor over the hidden texts to reveal),
which is
and