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Maharashtra SSC Geometry HOTS Questions with Answers – Geometric Constructions | Class 10 Board Exam 2027

Practice set · 1 hr · 65 marks · for SSC 10th and similar exams

2027 60 minutes 65 marks Save WhatsApp

Sections

Most repeated board questions (2024–2026) 11 questions
HOTS: likely questions for 2027 12 questions

About this HOTS set

For Class 10 students, “HOTS” usually means the IMP questions: the ones most likely to be asked in the board exam. This page collects them for Geometric Constructions (Geometry, Chapter 4). This chapter is the safest marks in the paper: only three kinds of construction are asked, and they repeat almost word for word.

The first section has real questions from the six latest official MSBSHSE board papers (March 2024 to June 2026). The second section has new practice questions written by Doubtly in the same board pattern, including the constructions not asked recently. All answers, steps of construction and new questions are written by Doubtly. Figures are described in words; draw them neatly with a compass and ruler.

Marks from Geometric Constructions in recent board papers

Board paperQuestionsMarks
March 202427
July 202439
March 202527
July 202527
March 202627
June 202600

Counts are from our list of Geometric Constructions questions in each paper. In June 2026 a 3-mark tangent construction (included above) was set among the Circle questions, so this chapter shows 0 there.

Question types that repeat most

  • Tangents from an external point (radius r, point at distance d): asked in July 2024, March 2025 and March 2026.
  • Similar triangle to a given triangle: SSS type (March 2024, March 2025), SAS type with a given angle (July 2024, March 2026) and right-angled type (July 2025). This 3- or 4-mark question has come in every paper since March 2024 except June 2026.
  • Tangent at a point on the circle, including tangents at the ends of a chord (July 2024, July 2025, June 2026).
  • Tangents with a given angle between them (March 2024).

Exam tips

  1. Always write an analysis (calculate the sides of the new triangle from the ratio) before constructing; examiners give marks for it.
  2. Draw a rough figure first, then the accurate one. Keep all construction arcs visible; do not erase them.
  3. In the ray method, mark as many equal parts as the greater number of the ratio.
  4. For tangents from an outside point, check your drawing: each tangent should measure \(\sqrt{d^2 - r^2}\).

Chapters covered

Instructions

Solve on paper with a timer, then check against the solutions.

Most repeated board questions (2024–2026)

  1. Asked in: July 2024 board paper

    Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.

    2 marks See answer →

  2. Asked in: March 2025 board paper (the same type was asked in July 2024 and March 2026)

    Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.

    3 marks See answer →

  3. Asked in: March 2026 board paper

    Draw a circle with centre O and radius 3.5 cm, take a point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.

    3 marks See answer →

  4. Asked in: July 2025 board paper

    Draw a circle with centre O of radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. Construct tangents at point M and N to the circle.

    3 marks See answer →

  5. Asked in: June 2026 board paper (set among the Circle questions that year)

    Draw a circle of radius 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at point P and Q. Write your observation about the tangents.

    3 marks See answer →

  6. Asked in: March 2024 board paper (same SSS type with ratio 2 : 3 in March 2025)

    \(\Delta ABC \sim \Delta LMN\). In \(\Delta ABC\), AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct \(\Delta ABC\) and \(\Delta LMN\) such that \(\dfrac{BC}{MN} = \dfrac{5}{4}\).

    3 marks See answer →

  7. Asked in: March 2025 board paper

    \(\Delta ABC \sim \Delta PQR\). In \(\Delta ABC\), AB = 3.6 cm, BC = 4 cm and AC = 4.2 cm. The corresponding sides of \(\Delta ABC\) and \(\Delta PQR\) are in the ratio 2 : 3. Construct \(\Delta ABC\) and \(\Delta PQR\).

    4 marks See answer →

  8. Asked in: July 2024 board paper

    \(\Delta LMN \sim \Delta LQP\). In \(\Delta LMN\), LM = 3.6 cm, \(\angle L = 50^\circ\), LN = 4.2 cm and \(\dfrac{LM}{LQ} = \dfrac{4}{7}\). Construct \(\Delta LQP\).

    4 marks See answer →

  9. Asked in: March 2026 board paper

    \(\Delta ABC \sim \Delta ADE\). In \(\Delta ABC\), AB = 6.3 cm, \(\angle CAB = 50^\circ\), AC = 5.6 cm and \(\dfrac{AB}{AD} = \dfrac{7}{5}\). Construct \(\Delta ADE\).

    4 marks See answer →

  10. Asked in: July 2025 board paper

    \(\Delta ABC \sim \Delta PBR\), BC = 8 cm, AC = 10 cm, \(\angle B = 90^\circ\), \(\dfrac{BC}{BR} = \dfrac{5}{4}\), then construct \(\Delta PBR\).

    4 marks See answer →

  11. Asked in: March 2024 board paper

    Draw a circle with centre O having radius 3 cm. Draw tangent segments PA and PB through the point P outside the circle such that \(\angle APB = 70^\circ\).

    4 marks See answer →

HOTS: likely questions for 2027

  1. To construct tangents to a circle with centre O from an external point P, after drawing seg OP the next step is to

    1. (A) bisect seg OP
    2. (B) draw a perpendicular to OP at P
    3. (C) trisect seg OP
    4. (D) draw a tangent at O
    1 mark See answer →

  2. \(\Delta ABC \sim \Delta PBR\) and \(\dfrac{AB}{PB} = \dfrac{3}{5}\). To construct \(\Delta PBR\) by dividing a ray from B into equal parts, the number of equal parts to be marked is

    1. (A) 3
    2. (B) 5
    3. (C) 8
    4. (D) 2
    1 mark See answer →

  3. How many tangents can be drawn to a circle through a point on the circle?

    1. (A) 0
    2. (B) 1
    3. (C) 2
    4. (D) infinitely many
    1 mark See answer →

  4. A point P is 5 cm from the centre of a circle of radius 3 cm. Without drawing, find the length of each tangent from P.

    1 mark See answer →

  5. Two tangents drawn from an external point P to a circle with centre O make an angle of 80° with each other. Find the angle between the radii drawn to the points of contact.

    1 mark See answer →

  6. Draw seg AB of length 7.5 cm and divide it internally in the ratio 3 : 2.

    2 marks See answer →

  7. Draw a circle of radius 2.8 cm. Take any point P on it and draw a tangent at P without using the centre of the circle.

    3 marks See answer →

  8. Draw a circle with centre C and radius 3 cm. Take point P such that CP = 7 cm and draw tangents from P. Measure the tangent segments and verify by calculation.

    3 marks See answer →

  9. Draw a circle with centre O and radius 3.4 cm. Draw a chord AB of length 6 cm. Draw tangents at A and B and let them meet at P. Measure \(\angle APB\) and \(\angle AOB\). What do you observe?

    3 marks See answer →

  10. \(\Delta XYZ \sim \Delta XLM\). In \(\Delta XYZ\), XY = 4.8 cm, YZ = 5.6 cm and XZ = 4.2 cm, and \(\dfrac{XY}{XL} = \dfrac{4}{3}\). Construct \(\Delta XYZ\) and \(\Delta XLM\).

    4 marks See answer →

  11. \(\Delta PQR \sim \Delta PMN\). In \(\Delta PQR\), QR = 5.4 cm, \(\angle Q = 60^\circ\), \(\angle R = 45^\circ\), and \(\dfrac{QR}{MN} = \dfrac{3}{4}\). Construct \(\Delta PQR\) and \(\Delta PMN\).

    4 marks See answer →

  12. Draw a circle with centre O and radius 3.5 cm. Draw tangents PA and PB from an external point P such that the angle between them is 60°. Also find the length of PO and of each tangent segment.

    4 marks See answer →