## Chapter 11: Constructions

Q1. 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

Ans:

Answer: (b) p + q

Q2. To divide a line segment PQ in the ratio 5 : 7, first a ray PX is drawn so that ∠QPX is an acute angle and then at equal distances points are marked on the ray PX such that the minimum number of these points is

(a) 5

(b) 7

(c) 12

(d) 10

Answer: c

Q3. 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 A_{1} A_{2} A_{3}, … are located at equal distances on the ray AX and the point B is joined to

(a) A_{4}

(b) A_{11}

(c) A_{10}

(d) A_{7}

Answer: b

Q4. 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) 145°

(b) 130°

(c) 135°

(d) 90°

Ans: a

Q5. When a line segment is divided in the ratio 2 : 3, how many parts is it divided into?

(a) 2/3

(b) 2

(c) 3

(d) 5

Ans: (d) 5

Q6. 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

**Answer: (B)**

Q7. To construct a triangle similar to given ΔABC with its sides 8585 of the corresponding sides of ΔABC, draw a ray BX such that ∠CBX is an acute angle and X is one 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) 3

(b) 5

(c) 8

(d) 13

Ans: c) 8

Q8. 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^{0}

**Answer: (D)**

Q9. 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°

**Answer: (D)**

Q10. Which theorem criterion we are using in giving the just the justification of the division of a line segment by usual method ?

(a) SSS criterion

(b) Area theorem

(c) BPT

(d) Pythagoras theorem

Ans: c) BPT

Q11. A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of ___________ from the centre.

(A) 5cm

(B) 2cm

(C) 3cm

(D) 3.5cm

**Answer: (A)**

Q12. To divide a line segment AB in the ratio 5:6, draw a ray AX such that ∠BAX is an acute angle, then drawa ray BY parallel to AX and the points A_{1}, A_{2}, A_{3},…. and B_{1}, B_{2}, B_{3},…. are located to equal distances on ray AX and BY, respectively. Then, the points joined are

(A) A_{5} and B_{6}

(B) A_{6} and B_{5}

(C) A_{4 }and B_{5}

(D) A_{5} and B_{4}

**Answer: (A)**