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 figure, a circle touches all the four sides of a quadrilateral $ABCD$. If $AB = 6$ cm, $BC = 9$ cm and $CD = 8$ cm, then find the length of $AD$.
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2.In the given diagram, the radius of the circle is $40\mathrm{~cm}$ and the length of the perpendicular drawn from its centre O to the chord AB is $24\mathrm{~cm}$. Identify the length of the chord AB.
- A.32 cm
- B.48 cm
- C.64 cm
- D.80 cm
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3.In the circle with centre $O$, if $\angle ADB = 20^{\circ}$ what is the value of angle $\angle BAC$?
- a.$30^{\circ}$
- b.$70^{\circ}$
- c.$60^{\circ}$
- d.$50^{\circ}$
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4.The radii of two concentric circles are 17 cm and 10 cm. A line segment PQRS cuts the larger circle at P and S and the smaller circle at Q and R. If QR = 12 cm, find the length of PQ.
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5.In the adjoining figure, ABCD is a cyclic quadrilateral, ∠CBQ = 48° and a = 2b. Identify the labelled angle in the diagram that corresponds to the value of b.
- A.∠BCQ = 28°
- B.∠ABP = 28°
- C.∠BAP = 28°
- D.∠CBQ = 28°
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