CBSE Class 10 Maths: Constructions — Compass & Ruler Notes 2026

Division of a Line Segment

• Divide line AB in ratio m:n: draw ray AX at acute angle; mark (m+n) equal arcs on AX; join last point to B; draw parallel to this through mth point
• Dividing in ratio 3:2: mark 5 equal arcs (3+2); join 5th to B; draw parallel through 3rd arc point
• Justification: Basic Proportionality Theorem (BPT) ensures accuracy of construction

Construction of Tangent from External Point

• Draw circle with centre O; mark external point P; join OP; find midpoint M of OP; draw circle with MO as radius
• New circle cuts original at T₁ and T₂; PT₁ and PT₂ are two tangents from P
• Verify: OT₁ ⊥ PT₁ (tangent perpendicular to radius at point of contact)

Constructing a Similar Triangle

• Construct triangle similar to given triangle with scale factor m/n
• If scale factor > 1 (larger): mark m arcs on extended ray; if < 1 (smaller): mark m of n arcs
• Step: draw ray from A; mark n equal parts; join last point to C; draw parallels to get C'; same for B'

Tangent to Circle at a Point on Circle

• Given point P on circle with centre O: construct line perpendicular to OP at P
• Steps: draw OP; construct perpendicular at P using compass (bisect 180° arc or use right angle method)
• Result: tangent at P is unique and perpendicular to radius

Measurement Accuracy Tips

• Use sharp pencil; set compass to accurate radius; all arcs must be clearly visible
• Label all points (A, B, C, O, X, T₁) as instructed in the question
• CBSE construction questions: 4 marks; 2 marks for correct procedure, 2 for accurate diagram

CBSE Exam Notes

• Constructions Chapter: typically 1 question (4–5 marks) in CBSE Board exam
• Division of line segment and tangent from external point are most frequently asked
• Justify your construction: state the theorem (BPT, tangent-radius) used; 1 mark for justification