Police say a family friend found the three Sunday night at a home in North Royalton, south of Cleveland.
A North Canton man already facing murder charges in the deaths of a Stark County couple is now charged in the killings of a North Royalton woman and her two daughters.
Brinkman was arrested early Tuesday after a nine-hour standoff on Valley Forge Drive in Brunswick.
Brinkman was with evidence linking him to the Stark County crime scene when officers arrested him Tuesday morning in Brunswick, Loeding said. He is in custody of North Royalton Police Department.
Police on Monday identified the victims as 45-year-old Suzanne Taylor and her daughters, 21-year-old Taylor Pifer and 18-year-old Kylie Pifer.
OH police say a suspect in the deaths of a mother and her two adult daughters may also have been involved in a separate double homicide nearby.
Court records don't list an attorney for Brinkman. Brinkman is charged in the deaths of a married couple in Lake Township - Rogell Eugene John, 71, and Roberta Ray John, 64. Police say the women may have died a day before their bodies were found. It appears they were shot, the sheriff said.
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Brinkman was later also linked to the murder of a North Canton couple whose bodies were found in their home several hours before the standoff began.
No further details were available on the North Royalton case Tuesday afternoon.
Brinkman had also allegedly dated the couple's daughter, Maier said.
Mr. Brinkman was watching the house while they were away, the sheriff said.
Brinkman was thought to be an employee of a business owned by the Johns, but Maier said he did not have details about the business or how long Brinkman had been an employee.
Police officers forced entry into the home this morning and were able to take Brinkman into custody by utilizing a stun gun, police said.
Brinkman, a former Medina resident, has convictions in Cuyahoga County from 1998 and 1999 on four counts of receiving stolen property in three separate incidents. He was sentenced in February 2000 and was released from prison in September 2000.