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BX/XD=? AB diameter of circle , AC = AM, CD = AB

Source: Switzerland - 2022 Swiss Final Round p1

November 17, 2022

ratiogeometry

Problem Statement

Let

k

be a circle with centre

M

and let

AB

be a diameter of

k

. Furthermore, let

C

be a point on

C

such that

A

. Let

D

be the point on the line

AC

such that

CD = AB

and

C

lies between

BC

and

D

. Let

E

be the second intersection of the circumcircle of

BCD

with line

AB

and

F

be the intersection of the lines

ED

and

BC

. The line

AF

cuts the segment

BD

in

X

. Determine the ratio

BX/XD

.

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