Take it on the chin
Stand up undaunted to criticism, suffering, or punishment.
‘Take it on the chin’ comes from the sport of boxing, and refers to a boxer receiving a hard blow on the chin and receiving it well. Figuratively, it means to receive the full force of something punishing. Example: “Why do I have to take it on the chin for something I didn’t do?”
A boxer learns to defend against letting a punch get to his head, because taking a hit on the chin is to risk being knocked out. He defends by catching punches on his gloves, on on his elbows, or any place other than the chin.
Thus, in general, taking something on the chin is not a good thing. It means you take the full hit of it. On the other hand, if you willingly take something on the chin, without turning away, it’s a brave thing to do.
Toss (one’s) hat into the ring
Enter a competition or issue a challenge, or show willingness to join an enterprise. Now often used to enter a political race.
The expression comes from the boxing ring. In the early 1800s, someone who wanted to challenge a boxer would customarily throw his hat into the ring. This may have been necessary because of the crowds and noise at such events; nobody would hear if you just shouted or tried to push your way to the ring.
The earliest citation appears to be from an 1805 issue of The Sporting Magazine:
“Belcher appeared confident of success [in a boxing match], and threw his hat into the ring, as an act of defiance to his antagonist.”