Circle Theorems and Arc Length
Using angles, chords, tangents, and arc measures in circles
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?
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