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ED=CD or FD=CD, if BE=BF=(|CD^2 -BD^2|)/BC

Source: Norwegian Mathematical Olympiad 2021 - Abel Competition p4b

May 29, 2021

geometryequal segments

Problem Statement

The tangent at

C

to the circumcircle of triangle

ABC

intersects the line through

A

and

B

in a point

D

. Two distinct points

E

and

F

on the line through

B

and

C

satisfy

|BE| = |BF | =\frac{||CD|^2 - |BD|^2|}{|BC|}

. Show that either

|ED| = |CD|

|FD| = |CD|