MathDB

loci, equailaterals on sides All-Russian MO 1993 Regional (R4) 11.7

Source:

August 26, 2024

geometry

Problem Statement

Let

ABC

be an equilateral triangle. For an arbitrary line

\ell

. through

B

, the orthogonal projections of

A

and

C

\ell

are denoted by

D

and

E

respectively. If

D\ne E

, equilateral triangles

DEP

and

DET

are constructed on different sides of

\ell

. Find the loci of

P

and

T