Question

1. a circular track has a radius of 100 meters. if a runner covers an arc length of 200 meters, what is the measure of the central angle in radians?
2. which statement is false about a circles tangent line?
3. intersects the circle at exactly one point

Explanation:

Step1: Recall the arc - length formula

The formula for arc length \(s\) is \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius of the circle, and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

We are given that \(s = 200\) meters and \(r=100\) meters. Substituting these values into the formula \(s = r\theta\), we get \(200=100\theta\).

Step3: Solve for \(\theta\)

To solve for \(\theta\), divide both sides of the equation \(200 = 100\theta\) by \(100\). So, \(\theta=\frac{200}{100}=2\) radians.

Answer:

\(2\) radians