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.

AND:
OR:
NO:

Found problems: 628

Estonia Open Senior - geometry, 2003.1.2
Tags: geometry , angles , trigonometry , 3D geometry
Four rays spread out from point $O$ in a $3$-dimensional space in a way that the angle between every two rays is $a$. Find $\cos a$.

2016 Bulgaria JBMO TST, 1
Tags: geometry , geometric inequality , angles , cyclic quadrilateral
The quadrilateral $ABCD$, in which $\angle BAC < \angle DCB$ , is inscribed in a circle $c$, with center $O$. If $\angle BOD = \angle ADC = \alpha$. Find out which values of $\alpha$ the inequality $AB <AD + CD$ occurs.

Estonia Open Junior - geometry, 2002.2.3
Tags: geometry , angles , equal segments
In a triangle $ABC$ we have $|AB| = |AC|$ and $\angle BAC = \alpha$. Let $P \ne B$ be a point on $AB$ and $Q$ a point on the altitude drawn from $A$ such that $|PQ| = |QC|$. Find $ \angle QPC$.