i dont know how to start this please help its precalculus

Question

A small radio transmitter broadcasts in a 41 mile radius. If you drive along a straight line from a city 53 miles north of the transmitter to a second city 49 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

 ____  miles

Answer 1

Start by drawing and labeling a diagram.

A circle centered at (0, 0) with intercepts of (0, 41), (41, 0), (0, -41), and (-41, 0)

Label the north city at (0, 53) and the east city at (49, 0)

Determine the equation of the line passing through the two cities.

The equation of the edge of the transmission is

x² + y² = 41²

Determine the intersection of the city line and the circle..

Determine the distance between the two intersections.

Subtract that distance from the distance between the two cities.

This problem is solved with all of the techniques taught in Algebra 2.