NCERT Class 10 Maths Constructions Questions

(A) Main Concepts and Results
• Division of a line segment internally in a given ratio.
• Construction of a triangle similar to a given triangle as per given scale factor which may be less than 1 or greater than 1.
• Construction of the pair of tangents from an external point to a circle.

(B) Multiple Choice Questions
Choose the correct answer from the given four options:

Sample Question 1 : To divide a line segment AB in the ratio p : q (p, q are positive
integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray
AX at equal distances such that the minimum number of these points is
(A) greater of p and q (B) p + q
(C) p + q – 1 (D) pq

Solution : Answer (B)

Sample Question 2 : To draw a pair of tangents to a circle which are inclined to each
other at an angle of 35°, it is required to draw tangents at the end points of those two
radii of the circle, the angle between which is
(A) 105° (B) 70° (C) 140° (D) 145°

Solution : Answer (D)

EXERCISE 10.1
Choose the correct answer from the given four options:
1. To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on
the ray AX such that the minimum number of these points is
(A) 8 (B) 10 (C) 11 (D) 12

2. To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A1, A2, A3, .... are located at equal
distances on the ray AX and the point B is joined to
(A) A12 (B) A11 (C) A10 (D) A9

3. To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points
A1, A2, A3, ... and B1, B2, B3, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are
(A) A5 and B6 (B) A6 and B5 (C) A4 and B5 (D) A5 and B4

4. To construct a triangle similar to a given ΔABC with its sides 3 /7 of the corresponding sides of ΔABC, first draw a ray BX such that ∠CBX is an
acute angle and X lies on the opposite side of A with respect to BC. Then locate points B1, B2, B3, ... on BX at equal distances and next step is to join
(A) B10 to C (B) B3 to C (C) B7 to C (D) B4 to C

5. To construct a triangle similar to a given ΔABC with its sides 8 /5 of the corresponding sides of ΔABC draw a ray BX such that ∠CBX is an acute
angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is
(A) 5 (B) 8 (C) 13 (D) 3

6. To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of
the circle, the angle between them should be
(A) 135° (B) 90° (C) 60° (D) 120°

Please refer to attached file for NCERT Class 10 Maths Constructions Questions