9

Part of 2023 LMT Fall

Problems(2)

2023 Fall LMT Team #9 circumcenter and centroid related

Source:

ABC

O

be the circumcenter and let

G

be the centroid. The line perpendicular to

OG

O

BC

M

M

G

A

are collinear and

OM = 3

. Compute the area of

ABC

OG = 1

2023 Fall LMT Speed p9 - k/2023

Source:

Find the least positive integer

k

\frac{k}{2023}

is written in simplest form, the sum of the numerator and denominator is divisible by

7

.
Proposed byMuztaba Syed