MathDB

Circumcircles and intersections madness

Source: Germany VAIMO 2015 - #3

July 11, 2015

geometrycircumcircleIntersection

Problem Statement

Let

ABC

be an acute triangle with

|AB| \neq |AC|

and the midpoints of segments

[AB]

and

[AC]

be

D

resp.

E

. The circumcircles of the triangles

BCD

and

BCE

intersect the circumcircle of triangle

ADE

in

P

resp.

Q

with

P \neq D

and

Q \neq E

. Prove

|AP|=|AQ|

.
(Notation:

|\cdot|

denotes the length of a segment and

[\cdot]

denotes the line segment.)

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