Question

A car speeding around a track left skid marks in the shape of an arc of a circle. Thechord distance between the endpoints of the skid marks is 550 feet. The chord is 100feet from the center of the circle.What is the radius of the arc made by the skid marks? Round to the nearest tenth.559.9 ft.256.2 ft.550 ft.540.8 ft.x ft.100 ft292.6 ft.

Answer 1

In the given problem, the chord of the circle forms right triangles with a perpendicular line that passes through the center of the circle. Therefore, the length of the chord is bisected and we get the following triangles:

We can use the Pythagorean theorem to determine the value of the radius:

$r^2=(\frac{550}{2})^2+100^2$

Solving the operations:

$\begin{gathered} r^2=275^2+100^2 \\ r^2=75625+10000 \\ r^2=85625 \end{gathered}$

Now we take the square root to both sides:

$\begin{gathered} r=\sqrt[]{85625} \\ r=292.6 \end{gathered}$

Therefore, the radius of the arc is 292.6 ft.