# Probability Involving Area

## Probability That A Randomly Selected Chord Exceeds The Length Of The Radius Of Circle

**Situation**

If a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle?

- Assume that the distance of the chord from the center of the circle is uniformly distributed.
A. 0.5 C. 0.866 B. 0.667 D. 0.75 - Assume that the midpoint of the chord is evenly distributed over the circle.
A. 0.5 C. 0.866 B. 0.667 D. 0.75 - Assume that the end points of the chord are uniformly distributed over the circumference of the circle.
A. 0.5 C. 0.866 B. 0.667 D. 0.75

## Probability that a Point Inside a Square Will Subtend an Obtuse Angle to Adjacent Corners of the Square

**Problem**

Point *P* is randomly chosen inside the square *ABCD*. Lines *AP* and *PB* are then drawn. What is the probability that angle *APB* is obtuse?