Geometry Circles Angles Arcs Quiz – Free PDF

Contents

This geometry circles angles arcs quiz asks 10 multiple-choice questions on circles: chords, arcs and inscribed angles, and each answer comes with a short explanation.

This 10-question quiz checks the core circle facts: similar circles, central and inscribed angles, semicircles, tangents, chords and inscribed quadrilaterals. Choose the one best answer for each question and read the explanation afterward.

GeometryCommon Core: G-C.A.1 · G-C.A.2

🎯 Circles: Chords, Arcs and Inscribed Angles – Geometry math quiz

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Question 1

Which statement about circles is true?

A Two circles are similar only if their radii are equal

B Any two circles are similar

C Two circles are similar only if they share a center

D Circles with different radii are never similar

Question 2

Arc \(AB\) measures \(100^{\circ}\). What is \(m\angle ACB\)?

Arc AB measures 100°.

A \(100^{\circ}\)

B \(50^{\circ}\)

C \(200^{\circ}\)

D \(25^{\circ}\)

Question 3

An inscribed angle intercepts an arc of \(98^{\circ}\). What is the measure of the inscribed angle?

A \(98^{\circ}\)

B \(196^{\circ}\)

C \(24.5^{\circ}\)

D \(49^{\circ}\)

Question 4

Segment \(AB\) is a diameter and \(m\angle A=25^{\circ}\). What is \(m\angle B\)?

Segment AB is a diameter.

A \(25^{\circ}\)

B \(90^{\circ}\)

C \(155^{\circ}\)

D \(65^{\circ}\)

Question 5

A tangent segment \(AP\) is 12 long and the radius \(OA\) is 9. What is \(OP\)?

A \(15\)

B \(21\)

C \(\sqrt{63}\)

D \(225\)

Question 6

Tangent segments \(PA\) and \(PB\) are drawn and minor arc \(AB\) measures \(100^{\circ}\). What is \(m\angle P\)?

Minor arc AB measures 100°.

A \(80^{\circ}\)

B \(100^{\circ}\)

C \(50^{\circ}\)

D \(40^{\circ}\)

Question 7

Quadrilateral \(ABCD\) is inscribed in a circle and \(m\angle A=78^{\circ}\). What is \(m\angle C\)?

A \(78^{\circ}\)

B \(90^{\circ}\)

C \(102^{\circ}\)

D \(282^{\circ}\)

Question 8

A chord is 16 units long in a circle of radius 10. How far is the chord from the center?

A chord and the perpendicular from the center.

A \(8\)

B \(2\)

C \(6\)

D \(\sqrt{164}\)

Question 9

Two chords of the same circle have equal length. Which must be true?

A Both chords pass through the center

B The chords are parallel

C The chords intersect at right angles

D Their intercepted minor arcs have equal measure

Question 10

A central angle and an inscribed angle intercept the same arc. The central angle measures \(148^{\circ}\). What does the inscribed angle measure?

A \(148^{\circ}\)

B \(37^{\circ}\)

C \(74^{\circ}\)

D \(296^{\circ}\)

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

All circles are similar: a translation and a dilation with factor \(\frac{r_2}{r_1}\) map one onto another.
A central angle equals its arc; an inscribed angle equals half its arc.
An angle inscribed in a semicircle measures \(90^{\circ}\).
A radius is perpendicular to a tangent, and a circumscribed angle is \(180^{\circ}\) minus its minor arc.
Opposite angles of an inscribed quadrilateral are supplementary.