Difference between revisions of "Mock USAMO by probability1.01 dropped problems"
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at <math>N</math>, prove that <math>MN, EF, and BC</math> concur. | at <math>N</math>, prove that <math>MN, EF, and BC</math> concur. | ||
''Reason: The whole incircle business seemed rather artificial. Besides, it wasn’t that difficult.'' | ''Reason: The whole incircle business seemed rather artificial. Besides, it wasn’t that difficult.'' | ||
− | + | [[Image:Mock_usamo.png]] | |
[[Mock USAMO by probability1.01 dropped problems/Problem 2|Solution]] | [[Mock USAMO by probability1.01 dropped problems/Problem 2|Solution]] | ||
Revision as of 16:45, 2 September 2006
Problem 1
Problem 2
In triangle ,
, let the incircle touch
,
, and
at
,
, and
respectively. Let
be a point on
on the opposite
side of
from
. If
and
meet at
, and
and
meet
at
, prove that
concur.
Reason: The whole incircle business seemed rather artificial. Besides, it wasn’t that difficult.
Solution