Circles: Arcs and Angles — Engineering Board Exam Practice Questions

18 free engineering board exam reviewer questions on Circles: Arcs and Angles (Plane Geometry), each with the correct answer and a worked solution.

  1. An inscribed angle intercepts an arc of 80°. Find the measure of the inscribed angle.
  2. A central angle of a circle measures 110°. Find the measure of the intercepted arc.
  3. Two chords intersect inside a circle, forming an angle of 55°. If one of the intercepted arcs measures 70°, find the other intercepted arc.
  4. 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.
  5. 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…
  6. An arc of a circle measures 72° and has a length of 8 cm. Find the radius of the circle.
  7. Find the area of a sector of a circle with radius 10 cm and a central angle of 60°.
  8. Find the length of a chord that subtends a central angle of 90° in a circle of radius 8 cm.
  9. Two circles of radius 10 have centers 10 units apart. Find the area common to both circles.
  10. A circular sector of radius 10 cm has an area of 50 cm2. Find its perimeter in cm.
  11. In a circle of radius 6, a chord subtends a central angle of 120°. Find the length of the chord.
  12. A tangent and a chord meet at a point on a circle and intercept an arc of 100°. Find the angle between the tangent and the chord.
  13. Two secants drawn from an external point intercept arcs of 140° (far) and 40° (near) on a circle. Find the angle between the secants.
  14. Two chords intersect inside a circle. One of the angles they form and its vertical angle intercept arcs of 70° and 110°. Find the measure…
  15. Find the area of the circular segment cut off by a chord that subtends a central angle of 90° in a circle of radius 10.
  16. Find the area of a sector of a circle of radius 12 with a central angle of 60°.
  17. An inscribed angle intercepts an arc of 80°. Find the inscribed angle.
  18. Find the length of an arc of a circle of radius 8 cm that subtends a central angle of 45°.