ICSE Class 10 Circles (Tangent and Cyclic Properties) — Mock Test (2027)
Free online mock test for Circles (Tangent and Cyclic Properties) (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Circles (Tangent and Cyclic Properties) chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.In the given figure, PQ is a transverse common tangent to two circles with centres A and B and of radii 5 cm and 3 cm respectively. If PQ intersects AB at C such that CP = 12 cm, calculate AB.
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2.Assertion: If in a circle, the radius of the circle is 3 cm and distance of a point from the centre of a circle is 5 cm, then length of the tangent will be 4 cm. Reason: (hypotenuse)² = (base)² + (height)² (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true.
- A.Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- B.Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- C.Assertion (A) is true but reason (R) is false.
- D.Assertion (A) is false but reason (R) is true.
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3.In the given figure $O$ is the centre of the circle and given that $AB = BC$. What are the values of $x$ and $y$?
- A.$45^{\circ}$ and $65^{\circ}$
- B.$20^{\circ}$ and $70^{\circ}$
- C.$70^{\circ}$ and $20^{\circ}$
- D.$65^{\circ}$ and $45^{\circ}$
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4.Two circles touch each other internally. The tangents are drawn to the two circles from any point on the common tangent. Which of the following statements is true about these tangents?
- A.The tangents from the point to both circles are equal in length.
- B.The tangent to the larger circle is twice as long as the tangent to the smaller circle.
- C.The tangent to the smaller circle is longer than the tangent to the larger circle.
- D.The lengths of the tangents depend on the distance between the centers of the circles only.
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5.In the given figure, O is the centre of the circle. If $\angle AOB = 90^\circ$ and $\angle ABC = 30^\circ$, then find $\angle CAO$.
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