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The deadly crash happened Wednesday morning in the 10800 block of Foy Street in the Eastex/Jensen area.
The driver of a tan Lincoln Continental was going northbound when he hit the man also traveling on Foy Street, according to police.
A witness told police that the driver didn't stop, and instead kept going to his residence with the bicycle stuck under the front of his car.
The witness wasn't going to let him get away, though. They followed the suspect to his home in the 3200 block of Cedar Hill Lane, where patrol officers eventually detained him.
The driver was evaluated, and authorities determined he was not impaired.
As for the victim, he was rushed to an area hospital where he was pronounced dead.
No charges have yet been filed, as an investigation is ongoing.