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

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.

Answer 2

Answer: 155.7

Step-by-step explanation:

Use what you know.

Segment AC is 130 ft

Segment CD is 70ft

If you use the Pythagorean Theorem, in this case being $r^{2}$ = $a^{2}$ + $b^{2}$

To find segment CE, you would do r-70

So, $r^{2}$ = $130^{2}$ + $(r-70)^{2}$

$r^{2}$ = 16,900 + $r^{2}$ -140r + 4900

Add the -140r to the left side and then get rid of the two $r^{2}$. Then Add 16,900 and 4900 together

You'll end up with 140r = 21,800

Divide 140 on each side.

Your final answer will be 155.7 (rounded to the nearest tenth)