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, PA is a tangent to the circle, PBC is a secant, and AD bisects angle BAC. Identify the part of the diagram that confirms triangle PAD is isosceles.
- A.PD = AD (two sides of triangle PAD are equal)
- B.PA = PB (tangent and secant segments are equal)
- C.∠PAD = ∠PAB (angle bisector creates equal angles)
- D.∠PBA = ∠PCA (angles in the same segment are equal)
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2.In the given figure,
ABCD is a cyclic quadrilateral. Which set of values correctly represents a, b, and c?- A.a = 105°, b = 13°, c = 62°
- B.a = 115°, b = 23°, c = 52°
- C.a = 95°, b = 13°, c = 72°
- D.a = 105°, b = 15°, c = 60°
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3.In Figure, $PQ$ is a chord of length $8\,\mathrm{cm}$ of a circle of radius $5\,\mathrm{cm}$ and centre $O$. The tangents at $P$ and $Q$ intersect at point $T$. Find the length of $TP$.
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4.In the given figure, $PA$ is a tangent from an external point $P$ to a circle with centre $O$. If $\angle POB = 115^\circ$, then perimeter of $\angle APO$ is
- a.$25^\circ$
- b.$20^\circ$
- c.$30^\circ$
- d.$65^\circ$
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5.AB and CD are two parallel chords of lengths 8 cm and 6 cm respectively. If they are 1 cm apart and lie on the same side of the centre of a circle, find the radius of the circle.
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