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: 701

1988 IMO Longlists, 40
Tags: ratio , rectangle , geometric transformation , homothety , circumcircle , symmetry , geometry
[b]i.)[/b] Consider a circle $K$ with diameter $AB;$ with circle $L$ tangent to $AB$ and to $K$ and with a circle $M$ tangent to circle $K,$ circle $L$ and $AB.$ Calculate the ration of the area of circle $K$ to the area of circle $M.$ [b]ii.)[/b] In triangle $ABC, AB = AC$ and $\angle CAB = 80^{\circ}.$ If points $D,E$ and $F$ lie on sides $BC, AC$ and $AB,$ respectively and $CE = CD$ and $BF = BD,$ then find the size of $\angle EDF.$