Class 10 Constructions Complete Guide 2027 — Step-by-Step Compass and Ruler Diagrams

In short: Constructions carries 4 marks in CBSE Class 10 Maths 2027 under the Geometry unit. The chapter has three construction types: dividing a line segment in a given ratio, constructing a triangle similar to a given triangle, and constructing tangents to a circle. These are hands-on geometry problems where you must know the exact compass-and-ruler steps. No formula needed — just a clear sequence of steps and a neat diagram.

Constructions is Chapter 11 in CBSE Class 10 Maths. It belongs to the Geometry unit (15 marks total) and carries about 4 marks. This is a unique chapter — it is the only one where you physically draw with a compass and ruler during the exam. No algebra, no formulas, no calculations. Just geometric steps executed precisely.

The board typically asks one 4-mark question from this chapter. It is either a similar triangle construction or a tangent construction. The marking is based on the accuracy and completeness of your construction — faint lines, missing arcs, or unmarked points lose marks. For the full marks breakdown, see the CBSE Class 10 chapter-wise weightage.

Construction 1: Dividing a Line Segment in a Given Ratio

Problem: Divide a line segment AB in the ratio m : n.

Steps (for ratio 3 : 2 as example):

1. Draw line segment AB of the given length
2. Draw a ray AX at any acute angle to AB (below or above AB)
3. Mark (m + n) = 5 equal arcs on AX: A₁, A₂, A₃, A₄, A₅
4. Join A₅ to B
5. Through A₃ (the m-th point), draw a line parallel to A₅B, meeting AB at point P
6. P divides AB in the ratio 3 : 2

Why it works: By the Basic Proportionality Theorem (Thales' theorem), a line drawn parallel to one side of a triangle divides the other two sides proportionally.

Key tip: The arcs on AX must be equally spaced. Use the same compass opening for all arcs. If the arcs are uneven, the ratio is wrong.

Construction 2: Similar Triangle (Scaled Up or Down)

Problem: Construct a triangle similar to a given triangle ABC with sides in the ratio m/n.

Two cases:

• Scale factor < 1 (m < n): The new triangle is smaller (e.g., 3/4 scale)
• Scale factor > 1 (m > n): The new triangle is larger (e.g., 5/3 scale)

Steps (for triangle similar to ABC with scale 3/4 — smaller):

1. Draw the given triangle ABC
2. Draw a ray BX at an acute angle to BC (on the opposite side of A)
3. Mark max(m, n) = 4 equal arcs on BX: B₁, B₂, B₃, B₄
4. Join B₄ to C
5. Through B₃ (the m-th point), draw a line parallel to B₄C, meeting BC at C'
6. Through C', draw a line parallel to CA, meeting BA at A'
7. Triangle A'BC' is similar to triangle ABC with ratio 3/4

Steps (for scale 5/3 — larger):

1. Draw the given triangle ABC
2. Draw a ray BX at an acute angle to BC
3. Mark 5 equal arcs on BX: B₁, B₂, B₃, B₄, B₅
4. Join B₃ to C (note: the n-th point, not m-th)
5. Through B₅, draw a line parallel to B₃C, meeting BC extended at C'
6. Through C', draw a line parallel to CA, meeting BA extended at A'
7. Triangle A'BC' is similar to ABC with ratio 5/3

Memory trick: "Smaller → join the larger number, draw through the smaller. Larger → join the smaller number, draw through the larger." The number you join to C is always the denominator (n). The number you draw through is always the numerator (m).

Construction 3: Tangents to a Circle

3a: Tangent at a Point on the Circle

Steps:

1. Draw the circle with centre O and mark point P on it
2. Join OP
3. At P, construct an angle of 90° to OP (using compass: draw arcs from P on OP, then bisect the angle)
4. The line through P perpendicular to OP is the tangent

Why 90°: By the tangent-radius theorem, the tangent is perpendicular to the radius at the point of contact. See the Circles chapter guide for the proof.

3b: Tangents from an External Point

Steps (given circle with centre O, radius r, and external point P):

1. Draw the circle and mark external point P
2. Join OP
3. Find the midpoint M of OP (construct the perpendicular bisector of OP)
4. With M as centre and MO as radius, draw a circle
5. This circle intersects the original circle at points A and B
6. Join PA and PB — these are the two tangents

Why it works: The circle with diameter OP passes through all points that subtend a 90° angle on OP. Points A and B are on both circles, so angle OAP = angle OBP = 90°, making PA and PB tangents (tangent ⊥ radius).

Board exam favourite: "Draw two tangents to a circle of radius 4 cm from a point 7 cm from the centre." You need to draw the circle (r = 4), mark the point (7 cm from centre), find midpoint of the join, draw the second circle, and connect.

Common Mistakes That Cost Marks

1. Using pen instead of pencil. Construction must be in pencil. Pen marks cannot be erased if you make an error. Some boards specifically penalise ink constructions.

2. Not showing construction arcs. The arcs you draw with the compass are part of the construction. Erasing them removes evidence of your method. Board examiners check for arcs — keep them visible.

3. Unequal arc spacing. When dividing a line segment, all arcs on the ray must be equally spaced. If you change the compass width between arcs, the division will be inaccurate and you lose marks for precision.

4. Missing labels. Every point must be labelled: A, B, C, A', C', O, P, M, etc. An unlabelled construction is hard to mark and you may lose step marks even if the drawing is correct.

5. Not writing the steps. Most board questions say "Write the steps of construction." If you draw perfectly but do not write the steps, you lose 1-2 marks. Always write numbered steps alongside your diagram.

6. Drawing at the wrong scale. If the question says "radius 3 cm" and you draw a circle with radius 2 cm, the tangent from a given distance will be wrong. Use a ruler and measure accurately.

4-Week Practice Plan

Week 1: Line Segment Division

• Read NCERT Section 11.1
• Practice dividing a line segment in ratios 2:3, 3:5, 4:3 — do each one twice
• Focus on equal arc spacing — same compass opening every time
• Write the steps while drawing

Week 2: Similar Triangle Constructions

• Read NCERT Section 11.2
• Practice both cases: smaller (scale 2/3, 3/4) and larger (scale 4/3, 5/2)
• Do at least 4 constructions — 2 smaller, 2 larger
• Time yourself: each construction should take 8-10 minutes including steps

Week 3: Tangent Constructions

• Read NCERT Section 11.3
• Practice tangent at a point on the circle — 3 times
• Practice tangents from an external point — 5 times (this is the most common board question)
• Practice with different radii and distances: (r=3, d=5), (r=4, d=7), (r=3.5, d=6)

Week 4: Board Paper Practice

• Solve construction questions from the last 5 years of CBSE board papers
• Time yourself: one full construction in 10-12 minutes (drawing + steps)
• Check accuracy: measure your tangent lengths — they should be equal (Theorem 2 from Circles)
• Final drill: one construction from each type without looking at steps

Quick Revision Card for Exam Day

• Line segment ratio m:n: Mark (m+n) arcs → join last to B → parallel through m-th point
• Similar triangle (smaller, m/n): Mark n arcs → join n-th to C → parallel through m-th
• Similar triangle (larger, m/n): Mark m arcs → join n-th to C → parallel through m-th (extend BC)
• Tangent from external point: Find midpoint M of OP → circle with centre M, radius MO → intersections give tangent points
• Tangent at point on circle: draw radius → perpendicular at point of contact
• ALWAYS: pencil, show arcs, label points, write steps, measure accurately

For practice identifying construction types and verifying your work, try Padhaao's AI tutor — it walks you through the logic behind each construction step.

Frequently Asked Questions

How many marks does Constructions carry in CBSE Class 10 Maths 2027?

Constructions carries approximately 4 marks in the CBSE Class 10 board exam 2027, as part of the Geometry unit. Typically one 4-mark question appears, asking for either a similar triangle construction or a tangent construction from an external point. The marking is based on accuracy of drawing, visibility of construction arcs, correct labelling, and written steps.

Do I need to write the steps of construction or just draw?

You must write the steps. Most board questions explicitly say "Write the steps of construction." Even if the drawing is perfect, missing steps can cost 1-2 marks. Write numbered steps on the left side and draw the construction on the right, or write steps below the diagram.

What is the most commonly asked construction in board exams?

Constructing two tangents to a circle from an external point is the most frequently asked construction. The typical format is "Draw a circle of radius r cm. From a point P at distance d cm from the centre, draw two tangents to the circle." You need the midpoint-circle method described above.

How do I ensure accuracy in constructions?

Use a sharp pencil, keep the compass tight (so it does not slip), measure all given lengths with a ruler before starting, and use the same compass width for all equal arcs. Do not erase construction arcs — examiners check them. After constructing tangents from an external point, measure both tangent lengths — they should be equal as a verification.

Can I use a protractor for constructions?

Only if the question requires measuring or constructing a specific angle. For the three standard Class 10 constructions (line division, similar triangle, tangents), you should use only a compass and straightedge. The constructions are designed to work without angle measurement. Using a protractor where a compass construction is expected may not earn full marks.

Constructions is the one chapter where neatness matters as much as knowledge. Know the steps, draw with precision, label everything, show your arcs, and write the method alongside your diagram.