MathDB

ABCD must be cyclic (with diameter AC)

Source: Baltic Way 2007

November 30, 2010

geometrycircumcirclegeometry proposed

Problem Statement

In a convex quadrilateral

ABCD

we have

ADC = 90^{\circ}

. Let

E

and

F

be the projections of

B

onto the lines

AD

and

AC

, respectively. Assume that

F

lies between

A

and

C

, that

A

lies between

D

and

E

, and that the line

EF

passes through the midpoint of the segment

BD

. Prove that the quadrilateral

ABCD

is cyclic.

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