Circle word problem

Question

A small radio transmitter broadcasts in a 24 mile radius. If you drive along a straight line from a city 31 miles north of the transmitter to a second city 33 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

Answer 1

find the two points where the line

y=-31x/33 +31

intersects the circle

x^2 +y^2 = 24^2

find the distance between those two points

x^2 + (-31x/33+31)^2 = 24^2

solve for x,

the two x solutions = the x coordinates of the two intersection points

plug those two x values into y -31x/33 + 31 to find the y coordinates of the intersection points

use the distance formula, the Pythagorean Theorem to calculate the distance betwen those two points