G285 2021 Fall Problem Set
Revision as of 01:35, 9 July 2021 by Geometry285 (talk | contribs)
Welcome to the Fall Problem Set! There are problems,
multiple-choice, and
free-response.
Problem 1
Larry is playing a logic game. In this game, Larry counts , and removes the number
for every
th move, skipping
for
, and then increments
by one. If
starts at
, what is
when Larry counts his
th integer? Assume
Problem 2
Let be a right triangle with right angle at
, and
. Let
denote the intersection of the cevian dropped from
onto
such that
. If the reflection of point
across
lies on the circumcircle of
as
, and $\sin(BAC)<\frac{5}[8}$ (Error compiling LaTeX. Unknown error_msg), find the smallest possible integer radius of the circumcircle of
.