This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 27

2004 Switzerland Team Selection Test, 10
Tags: altitude , triangle area , sum , geometry , area
In an acute-angled triangle $ABC$ the altitudes $AU,BV,CW$ intersect at $H$. Points $X,Y,Z$, different from $H$, are taken on segments $AU,BV$, and $CW$, respectively. (a) Prove that if $X,Y,Z$ and $H$ lie on a circle, then the sum of the areas of triangles $ABZ, AYC, XBC$ equals the area of $ABC$. (b) Prove the converse of (a).

1999 Singapore Senior Math Olympiad, 2
Tags: geometry , trigonometry , triangle area , area
In $\vartriangle ABC$ with edges $a, b$ and $c$, suppose $b + c = 6$ and the area $S$ is $a^2 - (b -c)^2$. Find the value of $\cos A$ and the largest possible value of $S$.