Question

A car goes around a turn too quickly, it can leave tracks that form an arc of a circle. By finding the radius of the circle, accident investigators can
estimate the speed of the car. To find the radius, accident investigators choose points A and B on the tire marks. Then, the investigators find the
midpoint C of AB. Use the diagram to find the radius r of the circle. Round your answer to the nearest tenth.

Answer 1

Check the picture below.

$r^2~~ = ~~100^2~~ + ~~(r-35)^2\implies r^2~~ = ~~100^2~~ + ~~\stackrel{\textit{\Large F~O~I~L}}{(r^2-70r+1225)} \\\\\\ r^2=10000+r^2-70r+1225\implies 0=10000-70r+1225 \\\\\\ 70r=10000+1225\implies 70r=11225\implies r=\cfrac{11225}{70}\implies r\approx 160.4$