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, $PQR$ is a right-angled triangle with $PQ = 3$ cm and $QR = 4$ cm. A circle is inscribed in the triangle, touching all its sides. Calculate the radius of the circle.
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2.In the given circle, chord QN is perpendicular to chord MP and ∠MNQ = 20°. Which of the following is the measure of ∠NQP?
- A.20°
- B.50°
- C.70°
- D.90°
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3.In the given figure, $O$ is the centre of the circle. Given that $\angle CEB = 40^{\circ}$ and $CE = EB$. What is the value of $x + y$?
- A.$145^{\circ}$
- B.$235^{\circ}$
- C.$255^{\circ}$
- D.$180^{\circ}$
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4.In the given figure, PA is a tangent to the circle, PBC is a secant, and AD bisects angle BAC. Identify the labelled part that confirms triangle PAD is isosceles.
- A.∠PAD = ∠PDA (angles opposite equal sides in ΔPAD)
- B.PA = PB (tangent and secant segments from external point)
- C.∠BAC = ∠CAD (AD is angle bisector only)
- D.∠PBA = ∠PAB (base angles of isosceles ΔPAB)
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5.Assertion: $PA$ and $PB$ are two tangents to a circle with centre $O$. Such that $\angle AOB = 110^\circ$, then $\angle APB = 90^\circ$. Reason: The length of two tangents drawn from an external point are equal. (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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