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# Challenge problems: Arc length (radians) 1

Solve three challenging problems that ask you to find arc length without directly giving you the arc measure.

## Problem 1

In the figure below, start overline, A, C, end overline is a diameter of circle P. The length of start overline, P, C, end overline is 25 units.
A circle that is centered around point P. Points A, B, and C are on the circle and line segment A C is a diameter. Line segments A P, B P and C P are radii of the circle that are twenty-five units long. Angle A P B is three over ten pi.
What is the exact length of B, C, A, start superscript, \frown, end superscript?

## Problem 2

In the figure below, the length of start overline, P, A, end overline is 3 units.
A circle that is centered around point P. Points A, B, C, D, and E are on the circle. Line segments A P, B P, C P, D P, and E P are radii of the circle are three units long. Angle A P B is eleven pi over eighteen. Angle C P D is pi over three. Angle C P D is a right angle.
What is the exact length of D, A, C, start superscript, \frown, end superscript on circle P?