Practice applying circle theorems and finding arc lengths using angle and radius relationships.
Read each problem carefully. Show your work and use circle theorems to justify your answers when needed.
Using angles, chords, tangents, and arc measures in circles
Math - Grade 9-12
- 1
A circle has a radius of 6 cm. Find the length of an arc with central angle 60 degrees.
- 2
In a circle, a central angle measures 120 degrees. What is the measure of its intercepted arc?
- 3
An inscribed angle intercepts an arc measuring 86 degrees. Find the measure of the inscribed angle.
- 4
A diameter of a circle intercepts an arc. What is the measure of an inscribed angle that subtends the diameter?
- 5
Two inscribed angles intercept the same arc. One angle measures 35 degrees. What is the measure of the other angle?
- 6
A chord is 8 cm from the center of a circle with radius 10 cm. Find the length of the chord.
- 7
In a circle, two congruent chords are given. What can you conclude about the arcs they intercept?
- 8
A tangent and a radius meet at the point of tangency. What is the measure of the angle between them?
- 9
From the same exterior point, two tangent segments are drawn to a circle. One tangent segment is 11 cm long. Find the length of the other tangent segment.
- 10
A circle has circumference 30π cm. Find the length of an arc whose measure is 144 degrees.
- 11
Two chords intersect inside a circle. The intercepted arcs measure 110 degrees and 50 degrees. Find the measure of the angle formed by the chords.
- 12
Two secants intersect outside a circle. The larger intercepted arc measures 160 degrees and the smaller intercepted arc measures 80 degrees. Find the exterior angle.
- 13
An inscribed quadrilateral has three angles measuring 88 degrees, 92 degrees, and 105 degrees. Find the fourth angle.
- 14
A circle has radius 9 m. Find the arc length of a 200 degree arc. Give your answer in terms of π.
- 15
In the same circle, arc AB measures 70 degrees and arc CD measures 70 degrees. What can you conclude about chords AB and CD?