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Quizzes > Quizzes for Business > Education

Circle Geometry and Compass Skills Quiz

Sharpen Your Circle Constructions and Compass Techniques

Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art promoting Circle Geometry and Compass Skills Quiz

Get ready to explore a circle geometry quiz designed to sharpen your compass skills and deepen your understanding of arcs, chords and tangents. This interactive quiz is perfect for learners eager to master compass constructions and circle theorems in a practical way. Educators and students can easily customise each question in our intuitive editor for targeted practice. Check out the Circle Geometry Quiz Class 9 or try the Geometry Angles Assessment Quiz for more practice. Browse other engaging quizzes to expand your geometry expertise today.

What is the measure of the arc intercepted by a central angle of 60° in a circle?
60°
180°
120°
90°
The measure of a central angle of a circle is equal to the measure of its intercepted arc. Therefore, a 60° central angle intercepts a 60° arc.
In a circle, an inscribed angle measures 40°. What is the measure of its intercepted arc?
100°
120°
80°
40°
The inscribed angle theorem states that an inscribed angle measures half of its intercepted arc. Thus, if the angle is 40°, the arc measures 80°.
In a circle, a radius drawn perpendicular to a chord has what effect on that chord?
It bisects the chord
It is parallel to the chord
It forms a tangent at the chord
It bisects the corresponding arc
A radius drawn perpendicular to a chord will always bisect the chord into two equal segments. This follows from the perpendicular bisector property in circle geometry.
Which tool is primarily used in compass-and-straightedge constructions to draw arcs for bisectors and angle constructions?
Ruler
Set square
Protractor
Compass
The compass is used to draw arcs and circles necessary for constructing perpendicular and angle bisectors. While a ruler draws straight lines, it cannot create the required arcs.
What is the relationship between a radius drawn to a point of tangency and the tangent line at that point?
They are parallel
They intersect at the center
They are perpendicular
They never meet
A tangent to a circle is perpendicular to the radius drawn to the point of tangency. This is a fundamental property of tangents in circle geometry.
A chord in a circle of radius 13 cm is 10 cm from the center. What is the length of the chord?
13 cm
26 cm
√69 cm
2√69 cm
By dropping a perpendicular from the center to the chord, we form a right triangle with legs 10 cm and half the chord. Half the chord is √(13²−10²)=√69, so the full chord is 2√69 cm.
What is the measure of an inscribed angle that intercepts a 150° arc?
75°
150°
100°
50°
An inscribed angle measures half the measure of its intercepted arc. Therefore, an inscribed angle intercepting a 150° arc measures 75°.
What point does the perpendicular bisector of any chord in a circle always pass through?
An endpoint of the chord
A point on the tangent
The midpoint of the arc
The center of the circle
The perpendicular bisector of a chord always passes through the center of the circle. It is equidistant from the endpoints of the chord, so it locates the center on that line.
Equal chords in the same circle subtend equal angles at the _____?
Other chord
Center of the circle
Point of tangency
Circumference of the circle
Equal chords in a circle are equidistant from the center, so they subtend equal central angles. This follows from the congruence of the isosceles triangles formed by the radii.
Two chords AB and CD intersect at E inside a circle. If arc AC measures 60° and arc BD measures 100°, what is the measure of ∠AEC?
80°
70°
90°
60°
The measure of an angle formed by two intersecting chords inside a circle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Here, ∠AEC = ½(60° + 100°) = 80°.
Two secants from point P intersect a circle at A, B and C, D respectively. If arc AC is 160° and arc BD is 40°, what is the measure of ∠APD?
100°
10°
80°
60°
The angle between two secants from an external point equals half the difference of the measures of the arcs they intercept: ∠APD = ½(160° − 40°) = 60°.
What is the first step in bisecting ∠ABC using compass and straightedge?
Place the compass at vertex B and draw an arc that cuts both rays of the angle
Draw a line from B to the midpoint of AC
Measure the angle using a protractor
Draw a perpendicular from B to AC
The initial step in angle bisection is to draw an arc centered at the angle's vertex that intersects both sides of the angle. These intersection points are then used for further arcs to locate the bisector.
From a point P outside a circle, two tangent segments PA and PB are drawn to the circle. What is true about their lengths?
PA equals PB
PA is greater than PB
PA is less than PB
PA plus PB equals a constant
Tangent segments drawn from an external point to a circle are congruent. Hence, PA and PB have equal lengths due to the tangent - tangent theorem.
Which chord of a circle has the greatest length?
Radius
Diameter
Secant
Tangent
The diameter is a chord that passes through the center of the circle, making it the longest possible chord. No other chord can exceed the diameter's length.
Which of the following is NOT a valid circle theorem?
An inscribed angle equals the measure of its intercepted arc
Opposite angles of a cyclic quadrilateral sum to 180°
A tangent is perpendicular to the radius at the point of contact
An angle in a semicircle is a right angle
An inscribed angle actually measures half the measure of its intercepted arc, not the full arc. All the other statements are standard circle theorems.
What is the first step in constructing a tangent to a circle from an external point P using compass and straightedge?
Draw a circle centered at P with arbitrary radius
Draw line segment PO connecting P to the center O of the circle
Construct the perpendicular to OP at P
Measure the distance from P to the circle's circumference
When constructing a tangent from an external point P, the initial step is to connect P to the center O of the given circle. This line PO serves as the base for locating the right triangle used to draw the tangent.
In cyclic quadrilateral ABCD, ∠A is 65° and ∠B is 110°. What is the measure of ∠C?
55°
110°
70°
115°
Opposite angles in a cyclic quadrilateral sum to 180°, so ∠A + ∠C = 180°. Since ∠A is 65°, ∠C = 180° − 65° = 115°.
Two concentric circles have radii of 13 cm and 5 cm. A chord of the larger circle is tangent to the smaller circle. What is the length of this chord?
12 cm
24 cm
18 cm
26 cm
The perpendicular distance from the center to the chord equals the smaller radius (5 cm), so half the chord length is √(13² − 5²) = √(169 − 25) = 12 cm. Thus, the full chord length is 24 cm.
At point A on a circle, a tangent meets chord AC such that the angle between them is 40°. What is the measure of the inscribed angle ABC, where B is on the circle opposite segment AC?
80°
20°
40°
60°
By the tangent - chord theorem, the angle between a tangent and a chord through the point of contact equals the inscribed angle in the opposite segment. Therefore, ∠ABC is also 40°.
When constructing the perpendicular bisector of a segment AB with a compass, the compass width should be set to:
A length greater than half of AB
Exactly half of AB
Equal to the length of AB
A length smaller than half of AB
To ensure the two arcs drawn from A and B intersect, the compass width must exceed half the length of segment AB. This guarantees two intersection points for the perpendicular bisector.
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Learning Outcomes

  1. Analyse circle theorems to solve angle problems accurately
  2. Master compass constructions including perpendicular and angle bisectors
  3. Apply properties of chords, tangents, and arcs in diagram analysis
  4. Identify relationships between central and inscribed angles
  5. Demonstrate precision in drawing circles and constructing tangents
  6. Evaluate circle-based proofs using geometric reasoning

Cheat Sheet

  1. Similarity of Circles - All circles are similar figures, meaning you can scale and translate one circle to perfectly match another, no matter its size. This fundamental idea lets you apply the same rules to any circle you meet, big or small. Embrace the power of similarity and watch your circle skills soar! Common Core State Standards: Circles
  2. Central vs. Inscribed Angles - A central angle measures exactly twice any inscribed angle that subtends the same arc, like a superhero doubling down on powers. Understanding this magical 2:1 ratio is crucial for cracking a ton of circle problems. Once you've got it, angle hunting becomes a breeze! Circle Geometry Theorems - GeoGebra
  3. Radius - Tangent Perpendicularity - The radius of a circle always meets the tangent at the point of tangency at a perfect right angle, like two friends giving each other a high-five. This neat trick is your go-to tool when constructing tangents or solving related challenges. Watch your compass come alive with right-angle magic! Common Core State Standards: Circles
  4. Inscribed & Circumscribed Circles - Practice using compass and straightedge to draw the inscribed (inside) and circumscribed (outside) circles of a triangle like a true geometric artist. These constructions deepen your understanding of triangle centers and key angles. Get hands-on and see geometry jump off the page! High School Geometry Common Core G.C.A.3 - Circle Constructions
  5. Cyclic Quadrilateral Angles - In a cyclic quadrilateral (one inscribed in a circle), opposite angles always add up to 180° - talk about perfect balance! This supplementary relationship makes solving angle puzzles super satisfying. Keep your quadrilateral cool and complementary! Circle Geometry - AMSI
  6. Chord Perpendicular Bisector - The perpendicular bisector of any chord will always pass through the circle's center, like a detective sniffing out the secret hub. Use this property to locate centers and tackle construction tasks with confidence. Your compass never looked so sharp! Circle Geometry Theorems - MathsFaculty
  7. Alternate Segment Theorem - The angle between a tangent and a chord through the point of contact equals the angle in the opposite arc's segment, creating a delightful angle match. Mastering this theorem turns tricky angle puzzles into child's play. Get ready for some angle-swapping fun! Circle Geometry and Theorems - GeoGebra
  8. External Tangent Construction - Crafting a tangent line from a point outside a circle using only compass and straightedge is like performing geometry magic. This skill has real-world applications from engineering to art. Practice it until your tangents are perfectly smooth! High School Geometry Common Core G.C.A.3 - Circle Constructions
  9. Intersecting Chords Theorem - When two chords cross inside a circle, the products of the lengths of their segments are equal - boom, instant equality! This theorem helps you solve many problems involving chord lengths with ease. Let the segment multiplications begin! Circle Geometry - AMSI
  10. Mohr - Mascheroni Theorem - Any compass-and-straightedge construction can actually be done with a compass alone, proving that sometimes less really is more. This surprising result highlights the versatility of the humble compass. Embrace your inner geometric minimalist! Mohr - Mascheroni theorem - Wikipedia
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