MathDB

11

Part of 2013 Online Math Open Problems

Problems(2)

2012-2013 Winter OMO #11

Source:

1/16/2013
Let AA, BB, and CC be distinct points on a line with AB=AC=1AB=AC=1. Square ABDEABDE and equilateral triangle ACFACF are drawn on the same side of line BCBC. What is the degree measure of the acute angle formed by lines ECEC and BFBF?
Ray Li
Online Math Openanalytic geometrygraphing linesslopetrigonometry
2013-2014 Fall OMO #11

Source:

10/30/2013
Four orange lights are located at the points (2,0)(2,0), (4,0)(4,0), (6,0)(6,0) and (8,0)(8,0) in the xyxy-plane. Four yellow lights are located at the points (1,0)(1,0), (3,0)(3,0), (5,0)(5,0), (7,0)(7,0). Sparky chooses one or more of the lights to turn on. In how many ways can he do this such that the collection of illuminated lights is symmetric around some line parallel to the yy-axis?
Proposed by Evan Chen
Online Math Open