Engineering Board Exam Reviewer · Circles: Arcs and Angles · hard
A circle has a diameter AB of length 4 m. Points C and D lie on the same semicircle such that angle ABC=25° and angle BAD=35°. Find the length of the minor arc CD.
- 2.094 m
- 1.047 m
- 4.189 m
- 3.665 m
Answer
A. 2.094 m
Solution
Since AB is a diameter, arc AC=2(25°)=50° and arc BD=2(35°)=70°. Arc CD=180°-50°-70°=60°. With radius 2 m: arc length =2≤ft(60×π/180 )=2π/3 2.094 m.
More Circles: Arcs and Angles questions
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- Find the area of a sector of a circle with radius 10 cm and a central angle of 60°.
- Find the length of a chord that subtends a central angle of 90° in a circle of radius 8 cm.
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- A central angle of a circle measures 110°. Find the measure of the intercepted arc.
- Two chords intersect inside a circle, forming an angle of 55°. If one of the intercepted arcs measures 70°, find the other intercepted arc.
- Two secants are drawn to a circle from an external point, forming an angle of 25°. If the far arc measures 90°, find the near arc.