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triangle $CSE$ is equilateral [Austria Regional 2018, Problem 2]

Source: Austrian Mathematics Olympiad Regional Competition (Qualifying Round) 2018, Problem 2

June 12, 2018

geometryEquilateral Triangleperpendicular bisectorChordsAustrianational olympiadAUT

Problem Statement

Let

k

be a circle with radius

r

and

AB

a chord of

k

such that

AB > r

. Furthermore, let

S

be the point on the chord

AB

satisfying

AS = r

. The perpendicular bisector of

BS

intersects

k

in the points

C

and

D

. The line through

D

and

S

intersects

k

for a second time in point

E

. Show that the triangle

CSE

is equilateral.
Proposed by Stefan Leopoldseder