How about you take the equation of the circle and the equation of the line and solve them simultaneously to get the two points where the car enters and then leaves the area. Then it should be a trivial exercise to find the distance between them.
A small radio transmitter broadcasts in a 61 mile radius. If you drive along a straight line from a city 81 miles north of the transmitter to a second city 83 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
How about you take the equation of the circle and the equation of the line and solve them simultaneously to get the two points where the car enters and then leaves the area. Then it should be a trivial exercise to find the distance between them.