A police officer shot a masked protester in an incident shown live on Facebook and a man was set on fire on Monday during one of the most violent days of clashes in Hong Kong since pro-democracy unrest erupted more than five months ago.Protesters, who had already begun a city-wide day of action aimed at paralysing the international financial hub, reacted to the morning shooting by rampaging through train stations, barricading streets and vandalising shops throughout the day.READ | Hong Kong police investigating videos of man set alightA masked assailant also doused a man with a flammable liquid and set him ablaze during an argument, with the horrifying scene captured on mobile phones and also posted online.Police said a protester carried out that attack and accused black-clad "rioters" of an array of other violent acts, including throwing a petrol bomb inside a train carriage."Continuing this rampage is a lose-lose situation for Hong Kong," police spokesperson John Tse said at a press conference in which he showed the video of the man being set alight, as well as a fire inside a train.No government concessionsREAD | Hong Kong student who fell during protest clashes diesAt the end of the business day, Hong Kong chief executive Carrie Lam held a press conference to denounce the violence and vow it would not lead to any government concessions."I am making this statement clear and loud here, that will not happen," Lam said.The footage of the shooting - broadcast live on Facebook by a bystander - showed a police officer drawing a pistol as he tried to detain a masked person at a junction that had been blocked by protesters.Another unarmed masked protester then approached the officer and was shot, quickly falling to the ground.Authorities said he was in critical condition in hospital.Police chiefs defended the officer drawing his weapon and firing as a legitimate use of force given his fears for his safety.But protesters, who for months have accused police of using excessive force and demanded an independent inquiry into their actions, were incensed."I don't understand why police have to use that kind of brutality to hurt innocent people... it's just out of control," a 22-year-old IT worker, who gave her surname as Chan, told AFP as she joined angry crowds to protest in the area of the shooting.Monday's shooting was the third time protesters had been hit by live rounds fired by police. None of the shootings have resulted in deaths.Lam said the man set on fire was in a critical condition. She described that attack as "totally inhumane".Protesters ignored her pleas for calm with further rallies in multiple locations across the city on Monday night.Online forums used by the largely anonymous and leaderless movement also carried messages vowing another day of chaos on Tuesday.Hong Kong has endured 24 straight weeks of increasingly violent rallies aimed at securing greater democratic freedoms from China, which has ruled the city under a "one country, two systems" framework since its handover from the British in 1997.