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CBSE Class 10 Mathematics Worksheet

1.

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 3/4 of the corresponding sides of the first triangle?

2.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths?

3.

A pair of tangents can be constructed to a circle inclined at an angle of

A)

TRUE

 B)

FALSE
4.

To draw a pair of tangents to a circle which are inclined to each other at an angle of , it is required to draw tangents at the end points of those two radii of the circle, the angle between which is_______.

A)

B)

C)

D)

5.

A pair of tangents can be constructed from a point P to a circle of radius 5 cm situated at a distance of 4 cm from the centre.

A)

TRUE

 B)

FALSE
6.

Divide a line segment PQ of length 7.2 cm into 5:6 ratio?

7.

By geometrical construction, it is possible to divide a line segment in the ratio

A)

TRUE

 B)

FALSE
8.

To divide a line segment AB in the ratio 4:5, first a ray AX is drawn so that 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)

4

 D)

9.

To draw tangents to a circle of radius ‘p’ from a point on the concentric circle of radius ‘q’, the first step is to find_____.

A)

mid point of q

 B)

mid point of p

 C)

mid point of q-p

 D)

10.

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm?

11.

To divide a line segment PQ in the ratio 3:2, a ray PX is drawn first such that is an acute angle and then points P1 , P2 , P3 , .... are located at equal distances on the ray PX and the point Q is joined to_____.

A)

P5

 B)

P2

 C)

P3

 D)

12.

To divide a line segment AB in the ratio 4 : 5, draw a ray AX such that 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)

A6 and B5

 B)

A4 and B5

 C)

A5 and B4

13.

Two distinct tangents can be constructed from a point P to a circle of radius r situated at a distance.

A)

r from centre

 B)

r/2 from centre

 C)

More than r from centre

14.

To draw a pair of tangents to a circle which are at right angles to each other, it is required to draw tangents at end points of the two radii of the circle, which are inclined at an angle of_______.

A)

B)

C)

D)

15.

Construct a tangent to a circle  of radius 3 cm at a point P on it without using the centre of the circle?

16.

A triangle similar to equilaretal triangle ABC of each side 5 cm and of scale factor 2/5 is drawn. The new traingle is equilateral.

A)

TRUE

 B)

FALSE
17.

To construct a triangle similar to a given with its sides 3/4 of the corresponding sides of draw a ray BX such that 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)

3

 B)

7

 C)

4

 D)

18.

In division of a line segment AB, any ray AX making angle with AB is_____.

A)

right angle

 B)

obtuse angle

 C)

ac

19.

Construct an isosceles triangle whose base 7 cm and altitude is 3.5 cm?

20.

To construct a triangle similar to a given with its sides 3/7 of the corresponding sides of , first draw a ray BX such that 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)

B7 to C

 C)

B3 to C

 D)

CBSE Class 10 Mathematics Worksheet

Answers

1.

  1. Construct triangle PQR using SSS criteria

  2. Locate 5  points Q1 , Q2 , Q3 , Q4  on QX so that QQ1 = Q1Q2 = Q2Q3 = Q3Q4

  3. Join Q3R and draw a line through Q3  parallel to Q5C to intersect QR at R′  

  4. Draw a line through R′ parallel to the line PR to intersect PQ at P′. Then, P′QR′ is the required triangle.

2.

  1. Draw a circle of radius 6 cm with centre O.

  2. Draw PO = 10 cm and bisect it. Let M be the midpoint of PO where is P is outside the circle.

  3. Taking M as centre and MO as radius, draw a circle. Let it intersect the given circle at the points Q and R.

  4. Join PQ and PR. Then PQ and PR are the required two tangents.

3.
Option B
4.
Option D
5.
Option B

6.

  1. Draw a line segment AB = 7.2 cm

  2. Locate 5 points A1 , A2 , A3 , A4 , A5, A6, A7, A8, A9, A10 and A11 on AX so that AA1 = A1 A2 = A2 A3 = A3 A4 = A4 A5 =  A5A6=  A6 A7=  A7 A8=  A9 A10=  A10 A11

  3. Join BA11

  4. Through the point A5, draw a line parallel to A11B at A5 intersecting AB at the point C. Then, AC : CB = 5 : 6

7.
Option B
8.
Option B
9.
Option A

10.

  1. With O as a centre and radius equal to 4 cm and 6 cm, two circles are drawn.

  2. P be any point on the circle of radius 6 cm and OP is joined.

  3. Perpendicular bisector of OP is drawn which cuts it at M.

  4. With M as a centre and OM as a radius, a circle is drawn which intersect the the circle of radius 4 cm at Q and R.

  5. PQ and PR are joined. Thus, PQ and PR are the two tangents.

11.
Option A
12.
Option C
13.
Option C
14.
Option D

15.

Draw a circle of radius 3 cm
2. Draw a chord PQ
4.Take any point R on the major arc PQ and join PR and QR
5. Make
6. PT is required tangent.

 

16.
Option A
17.
Option C
18.
Option C

19.

  1. Draw a line AB = 7 cm

  2. From mid point D of AB draw a line CD = 3.5 cm perpendicular to AB.

  3. Join AC and BC and ABC is the required triangle.

20.
Option B
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