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.Two parallel chords of the lengths 80 cm and 18 cm are drawn on the same side of the centre of a circle of radius 41 cm. Find the distance between the chords.
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2.In the given figure, O is the centre of the circle and ∠ABC = 55°. Calculate the values of x and y.
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3.If radii of two concentric circles are $4\,\mathrm{cm}$ and $5\,\mathrm{cm}$, then the length of each chord of one circle which is tangent to the other is
- a.$3\,\mathrm{cm}$
- b.$6\,\mathrm{cm}$
- c.$9\,\mathrm{cm}$
- d.$1\,\mathrm{cm}$
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4.In the given figure, PQ is a chord of length 8 cm of a circle with radius 5 cm. The tangents at P and Q intersect at T. What is the length of TP?
- A.3 cm
- B.20/3 cm
- C.5 cm
- D.8 cm
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5.In the given diagram, P is a point on a circle with centre O. If P is equidistant from the two radii OA and OB, which of the following statements correctly describes the relationship between the arcs AP and BP?
- A.Arc AP is twice the length of arc BP
- B.Arc AP is equal to arc BP
- C.Arc AP is half the length of arc BP
- D.Arc AP and arc BP are unrelated in length
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