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 and PR are tangents from P to a circle with centre O. If $\angle POR = 55^\circ$, then $\angle QPR$ is
- a.$35^\circ$
- b.$55^\circ$
- c.$70^\circ$
- d.$80^\circ$
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2.Calculate: (i) ∠CDB (ii) ∠ABC (iii) ∠ACB
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3.In the given figure, BC is parallel to DE and O is the centre of the circle. If ∠CDE = x°, which labelled angle in the diagram is equal to x°?
- A.∠BCD
- B.∠BAC
- C.∠AOB
- D.∠ACD
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4.In the given figure, $AB$ is a diameter and $AC$ is a chord of a circle such that $\angle BAC = 30^\circ$. The tangent at $C$ intersects $AB$ produced at $D$. Which of the following proves that $BC = BD$?
- A.$\angle BCD = \angle BDC = 30^\circ$
- B.$\angle ACD = 60^\circ$
- C.$\angle ABC = 45^\circ$
- D.$\angle BAC = \angle BCA$
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5.In the given figure, BQ and CR are the bisectors of ∠ABC and ∠ACB respectively. If ∠BAC = 56° and ∠ABC = 64°, find ∠QPR.
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