Question

If 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

I just encountered this question. Here's my answer.

Given:
Segment AC = 130 feet
Segment CD = 70 feet

I think that I'll be using the Pythagorean Theorem in finding the value of r. r will be the hypotenuse

Segment CE = (r - 70 feet)

r² = a² + b²
r² = 130² + (r-70)²
r² = 16,900 + (r-70)(r-70)
r² = 16,900 + r² - 70r - 70r + 4900
r² - r² + 140r = 16,900 + 4,900
140r = 21,800
r = 21,800/140
r = 155.71 feet

The radius of the circle is 155.71 feet.