Beginning in the mid-70s Japan expanded its influence in Korea.  China tried to support Korea but this led to political and military conflict with Japan. 

In the mid-80s a treaty was completed between the Manchu Dynasty and Japan. Both nations agreed to stay out of Korea. 

A religious rebellion in Korea forced the Korean King to request assistance from the Qing Emperor.  Japan objected to the intervention.  This resulted in the Sino/Japanese war of 1895.  This was an overwhelming victory for Japan.  China ceded to Japan, Taiwan, the Pescadores Islands, and the Southern portion of the Liaoning Peninsula in China.  Russia, France and Germany, however, soon thereafter intervened (a/k/a Triple Intervention) and forced Japan to return Liaoning Peninsula to China. 

In 1900, the Boxer Sect rebelled in China.  This was an anti-foreigner, xenophobic uprising.  An eight-nation coalition was needed to suppress the uprising.   These last two events further proved that the Manchus were unable to cope with the challenges of the time.