Circles

Topics in this chapter

• Circle Basics and Properties
• Chords and Perpendicular Bisectors
• Central and Inscribed Angles
• Cyclic Quadrilaterals and Concyclic Points
• Intersecting and Concentric Circles
• Circle-Based Geometric Applications

Cheat sheet

Practice questions

1. Question 1Q-7741EF

   If a line intersects two concentric circles with center O at points A, B, C, and D in that order, which of the following is always true regarding the lengths of line segments?

   1. A.AB = CD
   2. B.AC = BD
   3. C.AD = BC
   4. D.AB > CD
   See the answer and solution
2. Question 2Q-BF59E4

   The angle subtended by an arc at the center is _______ the angle subtended by it at any point on the remaining part of the circle.

   1. A.half
   2. B.equal to
   3. C.twice
   4. D.four times
   See the answer and solution
3. Question 3Q-ECC9D0

   In a circle of radius 5 cm, AB and CD are two parallel chords of lengths 6 cm and 8 cm respectively, and they lie on opposite sides of the center. What is the distance between the two chords?

   1. A.7 cm
   2. B.6 cm
   3. C.5 cm
   4. D.4 cm
   See the answer and solution
4. Question 4Q-4C71F0

   If angles A, B, C, and D of a cyclic quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, what type of quadrilateral is ABCD?

   1. A.Parallelogram
   2. B.Trapezium
   3. C.Kite
   4. D.Square
   See the answer and solution
5. Question 5Q-4595F5

   If $ABCD$ is a cyclic quadrilateral such that $\angle A = 80^\circ$, then the measure of $\angle C$ is:

   1. A.80°
   2. B.100°
   3. C.180°
   4. D.10°
   See the answer and solution