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center of circles construction only by ruler

Source: Sharygin Geometry Olympiad 2014 Correspondence Round P17

August 1, 2018

geometryconstructionCircumcenter

Problem Statement

Let

AC

be the hypothenuse of a right-angled triangle

ABC

. The bisector

BD

is given, and the midpoints

E

and

F

of the arcs

BD

of the circumcircles of triangles

ADB

and

CDB

respectively are marked (the circles are erased). Construct the centers of these circles using only a ruler.