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equal circumcircles wanted, starting with a parallelogram

Source: Switzerland - Swiss MO 2012 p6

July 16, 2020

geometrycircumcircleequal circlesparallelogram

Problem Statement

Let

ABCD

be a parallelogram with at least an angle not equal to

90^o

and

k

the circumcircle of the triangle

ABC

. Let

E

be the diametrically opposite point of

B

. Show that the circumcircle of the triangle

ADE

and

k

have the same radius.