MathDB

2020 Team 15

Source:

February 2, 2020

team2020

Problem Statement

Let

ABC

be an acute triangle with

AB = 3

and

AC = 4

. Suppose

M

is the midpoint of segment

\overline{BC}

,

N

is the midpoint of

\overline{AM}

, and

E

and

F

are the feet of the altitudes of

M

onto

T

and

\overline{AC}

, respectively. Further suppose

BC

intersects

NE

at

S

and

NF

at

T

, and let

X

and

Y

be the circumcenters of

\triangle MES

and

\triangle MFT

, respectively. If

XY

is tangent to the circumcircle of

\triangle ABC

, what is the area of

\triangle ABC

?

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