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: 2

Estonia Open Senior - geometry, 1998.2.5
The plane has a semicircle with center $O$ and diameter $AB$. Chord $CD$ is parallel to the diameter $AB$ and $\angle AOC = \angle DOB = \frac{7}{16}$ (radians). Which of the two parts it divides into a semicircle is larger area?
chord area diameter geometry circumference

2015 NIMO Summer Contest, 10
Let $ABCD$ be a tetrahedron with $AB=CD=1300$, $BC=AD=1400$, and $CA=BD=1500$. Let $O$ and $I$ be the centers of the circumscribed sphere and inscribed sphere of $ABCD$, respectively. Compute the smallest integer greater than the length of $OI$. [i] Proposed by Michael Ren [/i]
incenter geometry circumference