2023 CMO(CHINA) Problems/Problem 5
Problem
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 |