Practise accurate ruler-and-compass constructions such as dividing a segment in a ratio and drawing tangents from an external point. This chapter is not listed in the CBSE 2026–27 Class X Mathematics board content; follow your school’s instructions.
Practise accurate ruler-and-compass constructions such as dividing a segment in a ratio and drawing tangents from an external point. This chapter is not listed in the CBSE 2026–27 Class X Mathematics board content; follow your school’s instructions.
Use a sharp pencil, unmarked straightedge and compass. Keep construction arcs visible, label every point, and do not erase the arcs used to justify the result. State the theorem that guarantees the construction.
To divide AB internally in ratio m:n, draw an auxiliary ray from A, mark m+n equal steps, join the last mark to B, and draw a parallel through the mth mark. The Basic Proportionality Theorem gives the required ratio.
For point P outside a circle with centre O, bisect OP at M. Draw the circle centred M through O; its intersections with the given circle are tangent points because the angle in a semicircle is 90°.
These are original practice questions modeled on common board-exam patterns; they are not reproduced past-paper questions.
Question: Construct a point P dividing a 7 cm segment AB in ratio 2:5.
Solution: Draw AB=7 cm. From A draw an auxiliary ray and mark 7 equal steps. Join the seventh mark to B. Through the second mark draw a parallel to that join; its intersection with AB is P. Then AP:PB=2:5.
Question: Construct tangents from P to a circle with centre O, where OP=8 cm and radius=3 cm.
Solution: Draw OP and bisect it at M. Draw the circle centred M with radius MO; it cuts the given circle at T₁,T₂. Join PT₁ and PT₂. Since each angle OTᵢP subtends diameter OP, it is 90°, so each line is a tangent.
Construct the same 3:4 division using two independent drawings. Measure both resulting parts with a ruler and compare the ratios. Record likely sources of error such as unequal compass steps or a thick line.
Record: Write the aim, materials, steps, observations and conclusion in your notebook. Follow teacher supervision for any classroom activity.
Try each question before opening its solution.
Seven steps, because 3+4=7.
The contact point lies on the circle with diameter OP; the angle in a semicircle is a right angle.
The Basic Proportionality Theorem.
Aligned to the Class X Mathematics curriculum for 2026–27 and the NCERT Mathematics textbook. Always confirm any school-specific internal assessment with your teacher.