MathDB

CNCM Online R1P6

Source:

September 2, 2020

Problem Statement

In triangle

\triangle ABC

with

BC = 1

, the internal angle bisector of

\angle A

intersects

BC

at

D

.

M

is taken to be the midpoint of

BC

. Point

E

is chosen on the boundary of

\triangle ABC

such that

ME

bisects its perimeter. The circumcircle

\omega

of

\triangle DEC

is taken, and the second intersection of

AD

and

\omega

is

K

, as well as the second intersection of

ME

and

\omega

being

L

. If

B

lies on line

KL

and

ED

is parallel to

AB

, then the perimeter of

\triangle ABC

can be written as a real number

S

. Compute

\lfloor 1000S\rfloor

.
Proposed by Albert Wang (awang11)

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