ICSE Class 10 Constructions — Mock Test (2027)
Free online mock test for Constructions (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 Constructions 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.Draw a circle of radius $3.5\mathrm{cm}$. From a point $P$, $6\mathrm{cm}$ from its centre, draw two tangents to the circle. Which step is essential to construct the tangents?
- A.Draw a circle with diameter $OP$ to find points of tangency.
- B.Construct the angle bisector of $\angle OPA$ to locate the tangents.
- C.Find the midpoint of $OP$ and draw a perpendicular to locate tangents.
- D.Use the intersection of $OP$ and the circle as the point of tangency.
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2.Construct a triangle ABC with AB = 6 cm, BC = 8 cm, and median AM = 5 cm. Then construct the incircle of triangle ABC and measure its radius. What is the radius of the incircle?
- A.1.5 cm
- B.2.0 cm
- C.2.5 cm
- D.3.0 cm
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3.Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle as shown in the diagram
. Which labelled part in the diagram represents the radius of the inscribed circle?- A.The perpendicular distance from the incentre to any side of the triangle
- B.The distance from the incentre to any vertex of the triangle
- C.The length of the angle bisector from a vertex to the opposite side
- D.The distance between two sides of the triangle along a median
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4.Using ruler and compass, a triangle ABC is constructed with AB = 6 cm, ∠BAC = 120°, and AC = 5 cm. A circle is then drawn passing through points A, B, and C. What is the approximate radius of this circle?
- A.4.2 cm
- B.5.3 cm
- C.6.0 cm
- D.7.1 cm
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5.Construct a ΔPMN, given that MN = 5 cm, PN = 7 cm, and ∠PMN = 90°. After constructing the triangle, an incircle is drawn. What is the radius of this incircle?
- A.1.0 cm
- B.1.5 cm
- C.2.0 cm
- D.2.5 cm
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