MathDB

2019 G3: Isosceles Right Triangle in an Equilateral Triangle

Source:

January 27, 2019

2019geometry

Problem Statement

Let

ABC

be an equilateral triangle with side length

2

, and let

M

be the midpoint of

\overline{BC}

. Points

X

and

Y

are placed on

AB

and

AC

respectively such that

\triangle XMY

is an isosceles right triangle with a right angle at

M

. What is the length of

\overline{XY}