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## High school geometry

### Course: High school geometry>Unit 8

Lesson 7: Inscribed angles

# Challenge problems: Inscribed angles

Solve two challenging problems that apply the inscribed angle theorem to find an arc measure or an arc length.

## Problem 1

In the figure below, angle, A, B, C is inscribed in circle P. The length of start overline, P, C, end overline is 12 units. The arc length of A, C, start superscript, \frown, end superscript is start fraction, 68, divided by, 15, end fraction, pi.
What is the measure of angle, A, B, C in degrees?
degrees

## Problem 2

In the figure below, angle, A, B, C is inscribed in circle P. The length of start overline, P, C, end overline is 4 units.
What is the length of A, 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 rounded to the nearest hundredth.​
units