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## High school geometry

### Course: High school geometry>Unit 8

Lesson 3: Arc length (from degrees)

# Challenge problems: Arc length 1

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

## Problem 1

In the figure below, start overline, D, B, end overline and start overline, A, C, end overline are diameters of circle P. The length of start overline, P, B, end overline is 8 units.
A circle that is centered around point P. Points A, B, C, and D while line segments D B and A C are diameters. Line segments A P, P B, C P, and D P are radii of the circle. Segment P B is eight units long. The angle A P D is a sixty degree angle.
What is the length of D, C, start superscript, \frown, end superscript?

## Problem 2

In the figure below, the radius of circle P is 6 units.
A circle that is centered around point P. Points A, B, and C Line segments A P, P B, and C P are radii of the circle that are six units long. Segment P B is eight units long. The angle A P B is a one hundred eleven degree angle. The angle B P C is a one hundred twenty-nine degree angle.
What is the length of A, B, C, start superscript, \frown, end superscript
Either enter an exact answer in terms of pi or use 3, point, 14 for pi and enter your answer as a decimal.​

## Problem 3

In the figure below, start overline, B, C, end overline is a diameter of circle P. The length of start overline, B, P, end overline is 3 units.
A circle that is centered around point P. Points A, B, C, and D while line segments B C is a diameter. Line segments A P, P B, C P, and D P are radii of the circle. Segment P B is three units long. The angle A P D is a thirty-five degree angle. The angle A P B is a ninety degree angle. Major Arc A D is highlighted.
What is the length of A, C, D, start superscript, \frown, end superscript?
Either enter an exact answer in terms of pi or enter your answer as a decimal rounded to the nearest integer.​

## Problem 4

In the figure below, angle, A, P, B, \cong, angle, B, P, C. The length of start overline, P, B, end overline is 4 units.
A circle that is centered around point P. Points A, B, and C Line segments A P, P B, and C P are radii of the circle that are four units long. The angle A P C is a one hundred fifty-two degree angle.
What is the length of B, C, start superscript, \frown, end superscript on circle P?
Either enter an exact answer in terms of pi or use 3, point, 14 for pi and enter your answer as a decimal rounded to the nearest hundredth.​