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.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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2.An equilateral triangle of side 4 cm is drawn. Which step is NOT part of constructing its circumcircle?
- A.Draw perpendicular bisectors of two sides
- B.Find the intersection of the bisectors as centre
- C.Draw arcs of radius 4 cm from all vertices
- D.Draw circle with radius equal to distance from centre to vertex
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3.Construct $\Delta ABC, BC = 6\mathrm{cm}, \angle ABC = 45^{\circ}$ and perpendicular from $A$ to $BC$ is $3.5\mathrm{cm}$. To construct its circumcircle, which step is necessary?
- A.Draw the angle bisector of $\angle BAC$ to locate the centre.
- B.Draw perpendicular bisectors of $BC$ and $CA$ intersecting at $O$.
- C.Construct the incircle and use its radius for the circumcircle.
- D.Find the midpoint of $AB$ and use it as the centre of the circumcircle.
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4.In the given diagram
, an equilateral triangle with side 5.6 cm is shown. Which labelled point represents the centre of the circle that can be inscribed within this triangle?- A.The point where two medians intersect
- B.The point where two angle bisectors intersect
- C.The point where two altitudes intersect
- D.The midpoint of any side of the triangle
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5.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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