Circles — Practice Quiz
Karnataka Board · Class 9 · Mathematics
Try a 4-question quiz on Circles for Karnataka Board Class 9 Mathematics: tap an answer to check it and see why. 45 questions in the full chapter test.
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Quick Quiz: Circles
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If two equal chords AB and CD of a circle with center O subtend angles of 60° at the center, what can we conclude?
A chord AB is 8 cm from the center of a circle. If the perpendicular from center O to AB meets AB at point M, what is true about AM and MB?
In a circle, two chords PQ and RS are equidistant from the center. If PQ = 12 cm, what is the length of RS?
An arc PQ of a circle subtends an angle of 80° at the center. What angle does the same arc subtend at any point R on the major arc?
Sample Questions
In a semicircle, if A and B are endpoints of diameter and C is any point on the semicircle, what is ∠ACB?
Show answer
90°
Step 1: We have a semicircle with diameter AB and point C on the semicircle. Step 2: The arc AB (semicircle) subtends 180° at center O. Step 3: By Theorem 9.7, angle at circumference = (1/2) × central angle. Step 4: Therefore, ∠ACB = 180°/2 = 90°. This is known as 'angle in a semicircle is a right angle' - a fundamental property of circles.
Two points P and Q on a circle subtend equal angles at two other points R and S on the same side of chord PQ. What can we conclude about points P, Q, R, and S?
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They are concyclic
Step 1: We have chord PQ subtending equal angles at points R and S on same side, so ∠PRQ = ∠PSQ. Step 2: By Theorem 9.9, if a line segment subtends equal angles at two points on same side, all four points lie on a circle. Step 3: This means points P, Q, R, and S are concyclic (lie on the same circle). Step 4: The converse is also true - if points are concyclic, they subtend equal angles (angles in same segment are equal).
In a cyclic quadrilateral ABCD, if ∠A = 70°, what is ∠C?
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110°
Step 1: ABCD is a cyclic quadrilateral with ∠A = 70°, and we need to find ∠C. Step 2: By Theorem 9.10, opposite angles of a cyclic quadrilateral are supplementary (sum = 180°). Step 3: Since A and C are opposite angles: ∠A + ∠C = 180°. Step 4: Therefore, ∠C = 180° - 70° = 110°. This property helps identify cyclic quadrilaterals.
A chord of length 6 cm is at a distance of 4 cm from the center of a circle. What is the radius of the circle?
Show answer
5 cm
Step 1: Let chord AB = 6 cm, distance from center O to chord = 4 cm, perpendicular meets chord at M. Step 2: By perpendicular bisector property, AM = MB = 6/2 = 3 cm. Step 3: In right triangle OAM: OM = 4 cm, AM = 3 cm, OA = radius. Step 4: Using Pythagoras theorem: OA² = OM² + AM² = 4² + 3² = 16 + 9 = 25. Therefore, OA = 5 cm.
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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