2023 CMO Problems/Problem 5
Revision as of 04:34, 25 May 2024 by Anyu tsuruko (talk | contribs)
In an acute triangle is a point on the extension of
. Through
, draw lines parallel to
and
, denoted as
and
respectively, such that
and
. Let the circumcircle of
intersect
at point
. Prove:
(1) ;
(2) .
Solution 1
Proof for (1):
Let the side lengths of be
. We have
.
Let
.
Assume :
Assume :
Assume
Proof: (2)
~xiaohuangya|szm
See Also
2023 CMO(CHINA) (Problems • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All CMO(CHINA) Problems and Solutions |