CONSTRUCTIONS

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

Answer 1

(b) p + q

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°

Answer 2

(d) 145°

Question 3

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

Answer 3

(d) 12

Question 4

To divide a line segment AB in the ratio 4 : 7, 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

Answer 4

(b) A11

Question 5

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 B4 parallel to AX and the points A1, A2, A3, …….. and B1, B2, B3,………. are located at equal distances on ray AX and B4, respectively. Then the points joined are

(a) A5 and B6
(b) A6 and B5
(c) A4 and B5
(d) A5 and B4

Answer 5

(a) A5 and B6

Question 6

To construct a triangle similar to a given ΔABC with its sides 37 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

Answer 6

(c) B7 to C

Question 7

To construct a triangle similar to a given ΔABC with its sides 85 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. Then minimum number of points to be located at equal distances on ray BX is

(a) 5
(b) 8
(c) 13
(d) 3

Answer 7

b) 8

Question 8

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°

Answer 8

(d) 120°

Question 9

1. To divide a line segment AB in the ratio 3:4, 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) 5
   (b) 7
   (c) 9
   (d) 11

Answer 9

(b)7

Question 10

2. To divide a line segment AB of length 7.6cm in the ratio 5:8, a ray AX is drawn first such that ∠BAX forms 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) A5
   (b) A6
   (c) A10
   (d) A13

Answer 10

(d)A13

Question 11

3. To construct a triangle similar to a given ΔPQR with its sides 5/8 of the similar sides of ΔPQR, draw a ray QX such that ∠QRX is an acute angle and X lies on the opposite side of P with respect to QR. Then locate points Q1, Q2, Q3, … on QX at equal distances, and the next step is to join:
   (a) Q10 to C
   (b) Q3 to C
   (c) Q8 to C
   (d) Q4 to C

Answer 11

(c)Q8 to C

Question 12

4. To construct a triangle similar to a given ΔPQR with its sides, 9/5 of the corresponding sides of ΔPQR draw a ray QX such that ∠QRX is an acute angle and X is on the opposite side of P with respect to QR. The minimum number of points to be located at equal distances on ray QX is:
   (a) 5
   (b) 9
   (c) 10
   (d) 14

Answer 12

(b)9

Question 13

5. To construct a pair of tangents to a circle at an angle of 60° to each other, it is needed to draw tangents at endpoints of those two radii of the circle, the angle between them should be:
   (a) 100
   (b) 90
   (c) 180
   (d) 120

Answer 13

(d)120

Question 14

6. To divide a line segment PQ in the ratio m:n, where m and n are two positive integers, draw a ray PX so that ∠PQX is an acute angle and then mark points on ray PX at equal distances such that the minimum number of these points is:
   (a) M+n
   (b) M-n
   (c) M+n-1
   (d) Greater of m and n

Answer 14

(a)M+n

Question 15

7. To draw a pair of tangents to a circle which are inclined to each other at an angle of 45°, it is required to draw tangents at the endpoints of those two radii of the circle, the angle between which is:
   (a) 135
   (b) 155
   (c) 160
   (d) 120

Answer 15

(a)135

Question 16

8. 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) 3.5
   (b) 2.5
   (c) 5
   (d) 2

Answer 16

(c)5

Question 17

9. To construct a triangle ABC and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle. A ray AX is drawn where multiple points at equal distances are located. The last point to which point B will meet the ray AX will be:
   (a) A1
   (b) A2
   (c) A3
   (d) A4

Answer 17

(c)A3

Question 18

10. To construct a triangle similar to a given ΔPQR with its sides 3/7 of the similar sides of ΔPQR, draw a ray QX such that ∠QRX is an acute angle and X lies on the opposite side of P with respect to QR. Then locate points Q1, Q2, Q3, … on QX at equal distances, and the next step is to join:
    (a) Q10 to C
    (b) Q3 to C
    (c) Q7 to C
    (d) Q4 to C

Answer 18

(c)Q7 to C