**Problem 8:**

Four points are chosen in the order $A$, $B$, $C$, $D$ on a line such that there is a point $X$, not on that line, so that triangles $XAB$ and $XCD$ have the same area. If $AB = 8$ and $BC = 5$, find the length $AD$.

Please

Four points are chosen in the order $A$, $B$, $C$, $D$ on a line such that there is a point $X$, not on that line, so that triangles $XAB$ and $XCD$ have the same area. If $AB = 8$ and $BC = 5$, find the length $AD$.

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please**install LaTeX fonts** in your PC for better looking equations,

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Please

- Tahmid Hasan
**Posts:**665**Joined:**Thu Dec 09, 2010 5:34 pm**Location:**Khulna,Bangladesh.

the area and height(as they have the same vertex $X$) of $\delta XAB$ and $\delta XCD$ are same so $CD=8$

so $AD=AB+BC+CD=8+5+8=21$

so $AD=AB+BC+CD=8+5+8=21$

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