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 $AD$.
Rangpur Secondary 2011/8
Forum rules
Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
Re: Rangpur Secondary 2011/8
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 $AD=AB+BC+CD=8+5+8=21$
বড় ভালবাসি তোমায়,মা