How many practice questions are available for Circle Geometry?

SparkEd Math offers 60+ practice questions for Circle Geometry across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Circle Geometry content free on SparkEd Math?

Yes! All Circle Geometry content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Circle Geometry differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Circle Geometry problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Circle Geometry content aligned with the IB syllabus?

Yes, all Circle Geometry questions and lessons on SparkEd Math are fully aligned with the International Baccalaureate (MYP) (IB) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Circle Geometry — Class 9 IB (2025-26)

About Circle Geometry — Class 9 IB

Explore angle properties of circles, tangent-chord relationships, and inscribed angles. This topic is part of the IB Class 9 mathematics syllabus (chapter: Unit 5). On this page you can practice 59 questions across three difficulty levels — 20 easy, 20 medium, and 19 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Circle Geometry — solved examples for Class 9 IB

Example 1easy

Which of the following statements about a circle is always true?

A)All chords in a circle are equal in length to the radius.
B)The diameter is the longest chord in any given circle.
C)A tangent line intersects the circle at two distinct points.
D)An arc is always longer than the chord it subtends.

Step-by-step solution

A chord connects two points on the circumference. A diameter is a special type of chord that passes through the center of the circle.
Any other chord will be shorter than or equal to the diameter. If a chord does not pass through the center, it will be shorter than the diameter.
Therefore, the diameter represents the maximum possible length for a chord in a circle.

Answer: The diameter is the longest chord in any given circle.

Example 2medium

In a circle with centre O, points A, B, C are on the circumference. If ∠OAB = 35° and ∠OCB = 25°, find the measure of ∠AOC.

A)A) 60°
B)B) 70°
C)C) 120°
D)D) 140°

Step-by-step solution

In ΔOAB, OA = OB (radii), so ΔOAB is isosceles. Thus, ∠OBA = ∠OAB = 35°.
In ΔOBC, OB = OC (radii), so ΔOBC is isosceles. Thus, ∠OBC = ∠OCB = 25°.
Now, ∠ABC = ∠OBA + ∠OBC = 35° + 25° = 60°.
The angle subtended by arc AC at the circumference is ∠ABC. The angle subtended by arc AC at the centre is ∠AOC. According to the theorem, ∠AOC = 2 × ∠ABC = 2 × 60° = 120°.

Answer: C) 120°

Example 3hard

In a circle with center O, points A, B, C, D are on the circumference such that ABCD is a cyclic quadrilateral. If the angle subtended by the major arc ABC at the center O is 280°, what is the measure of ∠ADC?

A)70°
B)100°
C)110°
D)140°

Step-by-step solution

The angle subtended by the major arc ABC at the center O is 280°. This means the reflex angle ∠AOC = 280°.
The minor angle ∠AOC = 360° - 280° = 80°.
The angle ∠ABC is subtended by the minor arc AC at the circumference, so ∠ABC = (1/2) × minor ∠AOC.
$∠ABC = (1/2) × 80° = 40°.$
Since ABCD is a cyclic quadrilateral, the sum of opposite angles is 180°. Therefore, ∠ADC + ∠ABC = 180°.
$∠ADC = 180° - 40° = 140°.$

Answer: 140°

Practice questions on Circle Geometry

Q1.easy
In a circle with centre O, points A, B, and C are on the circumference. If the angle subtended by arc AC at the centre, ∠AOC, is 130°, what is the measure of the angle subtended by the same arc at any point B on the remaining part of the circumference (∠ABC)?
1. A)65°
2. B)130°
3. C)260°
4. D)100°
Show answer
Answer: 65°
Hint: Recall the theorem that relates the angle at the centre to the angle at the circumference when both are subtended by the same arc.
Q2.easy
A triangle ABC is inscribed in a circle such that side AC is the diameter of the circle. Which of the following statements must be true about ∠ABC?
1. A)∠ABC is always 90°.
2. B)∠ABC is always less than 90°.
3. C)∠ABC is always greater than 90°.
4. D)The measure of ∠ABC depends on the position of point B.
Show answer
Answer: ∠ABC is always 90°.
Hint: Consider the special case of the angle subtended by a diameter at any point on the circumference.
Q3.easy
Rhea is solving a problem where points A, B, C, D lie on a circle. She is given that ∠CAD = 35°. She concludes that ∠CBD = 70° because 'the angle at the circumference is half the other angle'. Identify the mistake in Rhea's reasoning.
1. A)Rhea's calculation is correct; ∠CBD should indeed be 70°.
2. B)Rhea should have concluded that ∠CBD = 35° because they are angles in alternate segments.
3. C)Rhea should have concluded that ∠CBD = 35° because they are angles subtended by the same arc in the same segment.
4. D)Rhea confused the relationship between angles at the circumference and the angle at the centre. There's no 'other angle' that is double ∠CAD in this context for ∠CBD.
Show answer
Answer: Rhea should have concluded that ∠CBD = 35° because they are angles subtended by the same arc in the same segment.
Hint: Focus on the theorem related to angles subtended by the *same arc* within the *same segment* of a circle.
Q4.medium
ABCD is a cyclic quadrilateral. Diagonals AC and BD intersect at P. If ∠DBC = 70° and ∠BAC = 40°, find the measure of ∠BCD. (Assume A, B, C, D are in order around the circle).
1. A)A) 70°
2. B)B) 80°
3. C)C) 110°
4. D)D) 140°
Show answer
Answer: A) 70°
Hint: Look for angles subtended by the same arc. Also, remember the property of opposite angles in a cyclic quadrilateral.
Q5.medium
A circular park has a diameter of 26 meters. A straight pedestrian bridge is built across the park, such that its midpoint is 5 meters away from the centre of the park. What is the length of the bridge?
1. A)A) 12 m
2. B)B) 13 m
3. C)C) 24 m
4. D)D) 25 m
Show answer
Answer: C) 24 m
Hint: The bridge acts as a chord. The distance from the centre to the bridge is the perpendicular distance, which bisects the chord. Use the Pythagorean theorem.
Q6.medium
From an external point P, two tangents PA and PB are drawn to a circle with centre O. If the radius of the circle is 6 cm and the length of the tangent PA is 8 cm, what is the area of quadrilateral OAPB?
1. A)A) 24 cm²
2. B)B) 48 cm²
3. C)C) 60 cm²
4. D)D) 72 cm²
Show answer
Answer: B) 48 cm²
Hint: Remember that the radius is perpendicular to the tangent at the point of contact. This forms right-angled triangles.
Q7.hard
In a circle, a triangle ABC is inscribed such that the tangent to the circle at point A is parallel to the chord BC. If ∠ABC = 70°, what is the measure of ∠ACB?
1. A)50°
2. B)60°
3. C)70°
4. D)80°
Show answer
Answer: 70°
Hint: Consider the relationship between angles formed by parallel lines and the Alternate Segment Theorem. How do these connect to the angles within the triangle?
Q8.hard
Chords AB and CD intersect at point P inside a circle. If AP = (x + 3) cm, PB = (x - 1) cm, CP = x cm, and PD = 4 cm. If AB is the diameter of the circle, what is the length of the radius?
1. A)4 cm
2. B)5 cm
3. C)6 cm
4. D)8 cm
Show answer
Answer: 4 cm
Hint: First, use the Intersecting Chords Theorem to find the value of x. Then, calculate the length of the diameter AB and subsequently the radius.
Q9.hard
In a cyclic quadrilateral ABCD, the diagonals AC and BD intersect at point P. If ∠DBC = 65°, ∠BAC = 35°, and ∠ACB = 40°, find the measure of ∠ADC.
1. A)70°
2. B)75°
3. C)80°
4. D)85°
Show answer
Answer: 75°
Hint: Remember that angles subtended by the same arc in a circle are equal. Use this property to find the component angles of ∠ADC.

These are 9 of the 59 questions available for Circle Geometry. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.