CBSE Class 10 Mathematics Constructions Assignment Set A

Question. To divide a line segment AB in ratio m: n (mand n are positive integers), draw a ray AX to that ∠BAX is an acute angle and the mark point on ray AX at equal distances such that the minimum number of these points is
(a) greater of m and n
(b) m + n
(c) m + n −1
(d) mn
Answer : B

Question. To divide a line segment AB in the ratio 4 : 5, first a ray AX is drawn making ∠BAX an acute angle and then points A₁ , A₂ , A₃ , . . at equal distances are marked on the ray AX and the point B is joined to
(a) A₄
(b) A ₅
(c) A₉
(d) A₇
Answer : C

Question. To divide a line segment AB in the ratio 3 : 5 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) 9
(c) 10
(d) 11
Answer : A

Question. The ratio of division of the line segment AB by the point P from A in the following figure is 

(a) 2 : 3
(b) 3 : 2
(c) 3 : 5
(d) 2 : 5
Answer : B

Question. In the given figure, find the ratio, when P divides AB internally.

(a) 3 : 2
(b) 2 : 3
(c) 4 : 3
(d) 3 : 4
Answer : D

Question. 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
Answer : B

Question. 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 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

Question. To divide a line segment AB in the ratio 6 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A₁ , A₂ , A₃, … are located equal distances on the ray AX and the point B is joined with
(a) A₁₂
(b) A₁₃
(c) A₁₀
(d) A₁₁
Answer : B

Question. A pair of tangents can be constructed froma point P to a circle of radius 3.5 cm, situated at a distance of 3 cm from the centre.
(a) True
(b) False
(c) Can’t determined
(d) None of the above
Answer : B

Question. From the following ratios, a line segment cannot be divided into A ratio.

Answer : C

Question. 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 : D

Question. A pair of tangents can be constructed to a circle inclined at an angle of 170°.
(a) True
(b) False
(c) Can’t determined
(d) None of the above
Answer : A

Question. To draw a pair of tangents to a circle which are inclined to each other at an angle of 30°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be
(a) 150°
(b) 90°
(c) 60°
(d) 120°
Answer : A

Question. If you draw a pair of tangents to a circle C(O, r) from point P such that OP = 2r, then the angle between the two tangents is
(a) 90°
(b) 30°
(c) 60°
(d) 45°
Answer : C

 

Answer : d. 90^o

Explanation: According to the question, the tangents are inclined at an angle of 180o - 90^o = 90^o

 

Q.- Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 cm from its centre. 

 

Answer :

Steps of construction:

1. Take a point O on the plane of the paper and draw a circle of radius 3.5 cm.

2. Mark a point P at a distance of 6.2 cm from the centre O and join OP.

3. Draw a right bisector of OP, intersecting OP at Q.

4. Taking Q as centre and OQ = PQ as radius, draw a circle to intersect the given circle at T and T'.

5. Join PT and PT' to get the required tangents.

Level 3

Q1- Draw a pair of tangents to a circle of radius 4.5cm which are inclined to each other at an angle of 45⁰

Q2- Draw a circle of radius 6cm, draw a tangent to this circle making an angle of 300 with a line passing through the centre.

Please click the link below to download CBSE Class 10 Mathematics Constructions Assignment Set A