Difference between revisions of "G285 2021 Fall Problem Set"
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==Problem 2== | ==Problem 2== | ||
− | Let <math>\triangle ABC</math> be a right triangle with right angle at <math>B</math>, and <math>AC=12</math>. Let <math>D</math> denote the intersection of the cevian dropped from <math>B</math> onto <math>AC</math> such that <math>DA=DC</math>. If the reflection of point <math>B</math> across <math>D</math> lies on the circumcircle of <math>\triangle ABC</math> as <math>E</math>, and <math>\sin(BAC)<\frac{5} | + | Let <math>\triangle ABC</math> be a right triangle with right angle at <math>B</math>, and <math>AC=12</math>. Let <math>D</math> denote the intersection of the cevian dropped from <math>B</math> onto <math>AC</math> such that <math>DA=DC</math>. If the reflection of point <math>B</math> across <math>D</math> lies on the circumcircle of <math>\triangle ABC</math> as <math>E</math>, and <math>\sin(BAC)<\frac{5}{8}</math>, find the smallest possible integer radius of the circumcircle of <math>\triangle EBA</math>. |
Revision as of 01:35, 9 July 2021
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
, find the smallest possible integer radius of the circumcircle of
.