If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

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?
Choose 1 answer:

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?
Choose 1 answer:

Problem 3

In the figure below, start overline, A, D, end overline and start overline, B, E, end overline are diameters of circle P. The length of start overline, P, B, end overline is 10 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 ten units long. Angle B P C is pi over three. Angle A P E is nineteen pi over thirty-six.
What is the exact length of C, D, start superscript, \frown, end superscript?
Choose 1 answer:

Want to join the conversation?