JERSEY CITY, New Jersey (WABC) -- Authorities say a man is under arrest in the murder of a woman whose body was found in a lake in New Jersey.The Hudson County Prosecutor's Office announced the arrest of 33-year-old Jorge Rios, of Jersey City, in connection with the homicide. Authorities confirm he is an undocumented immigrant from Honduras.Rios, who lives near the park, has been charged with murder, felony murder, kidnapping and aggravated sexual assault.Hudson County Sheriff's officers discovered the body March 24 in Lincoln Park after receiving a report. At that time, police did not suspect foul play.The victim was identified as 45-year-old Carolina Cano. Her roommate said she went out for a jog that morning and never returned.The Peruvian native lived just a few blocks away from the park. Her roommate said she went for a jog every morning before heading to work as a nanny.Video evidence seems to show the suspect following the victim as she was running in the park wearing headphones. City officials say the victim and suspect were unknown to each other and that it appears to be a random attack."Our understanding is that it was strangers, and he frequented the park, and we feel real comfortable that we have the right person based on his statements," said Jersey City Mayor Steve Fulop.Divers were out in the lake Tuesday searching for more evidence in the case."When you understand the video, the background, and the statements, this was just a horrible situation," Fulop said. "The entire circumstance was a terrible thing, and the prosecutors did a great job wrapping it up quick."The Medical Examiner's Office determined the cause of death to be homicidal violence including strangulation and water submersion.An arraignment and detention hearing for Rios is set for Thursday, April 4.Some in the community were on edge after the murder. Following the arrest, a community meeting will still take place to answer residents' questions about the case."Now that they do have a suspect, people should just continue to proceed with their lives as normal and know that we're all out there looking out for each other," said Jersey City Councilwoman Mira Prinz-Arey.Mayor Fulop said there will be added patrols in the Lincoln Park area to help residents feel more secure.----------