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 A1 A2 A3, … are located at equal distances on the ray AX and the point B is joined to
(a) A4
(b) A11
(c) A10
(d) A7
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) 1200
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 A1, A2, A3,…. and B1, B2, B3,…. are located to 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
Answer: (A)