# SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 chapter 4 - Geometric Constructions [Latest edition]

## Chapter 4: Geometric Constructions

Q.1 (A)Q.1 (B)Q.2 (A)Q.2 (B)Q.3 (A)Q.3 (B)Q.4Q.5
Q.1 (A)

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 Chapter 4 Geometric Constructions Q.1 (A)

#### Answer the following sub question [1 Mark]

Q.1 (A) | Q 1

Choose the correct alternative:

______ number of tangents can be drawn to a circle from the point on the circle.

• 3

• 2

• 1

• 0

Q.1 (A) | Q 2

Choose the correct alternative:

The tangents drawn at the end of a diameter of a circle are ______

• Perpendicular

• parallel

• congruent

• can’t say

Q.1 (A) | Q 3

Choose the correct alternative:

ΔLMN ~ ΔHIJ and "LM"/"HI" = 2/3 then

• ΔLMN is a smaller triangle

• ΔHIJ is a smaller triangle

• Both triangles are congruent

• Can’t say

Q.1 (A) | Q 4

Choose the correct alternative:

______ number of tangents can be drawn to a circle from the point outside the circle

• 2

• 1

• one and only one

• 0

Q.1 (A) | Q 5

Choose the correct alternative:

In the figure ΔABC ~ ΔADE then the ratio of their corresponding sides is ______

• 3/1

• 1/3

• 3/4

• 4/3

Q.1 (A) | Q 6

Choose the correct alternative:

Which theorem is used while constructing a tangent to the circle by using center of a circle?

• Converse of tangent – radius theorem

• Pythagoras theorem

• Converse of Pythagoras theorem

Q.1 (A) | Q 7

Choose the correct alternative:

ΔPQR ~ ΔABC, "PR"/"AC" = 5/7, then

• ΔABC is greater

• ΔPQR is greater

• Both triangles are congruent

• Can’t say

Q.1 (A) | Q 8

Choose the correct alternative:

∆ABC ∼ ∆AQR. "AB"/"AQ" = 7/5, then which of the following option is true?

• A–Q–B

• A–B–Q

• A-C–B

• A–R–B

Q.1 (B)

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 Chapter 4 Geometric Constructions Q.1 (B)

#### Solve the following examples [1 Mark]

Q.1 (B) | Q 1

Construct ∠ABC = 60° and bisect it

Q.1 (B) | Q 2

Construct ∠PQR = 115° and divide it into two equal parts

Q.1 (B) | Q 3

Draw Seg AB of length 9.7 cm. Take point P on it such that AP = 3.5 cm and A–P–B. Construct perpendicular to seg AB from point P.

Q.1 (B) | Q 4

Draw seg AB of length 4.5 cm and draw its perpendicular bisector

Q.1 (B) | Q 5

Draw seg AB of length 9 cm and divide it in the ratio 3 : 2

Q.1 (B) | Q 6

Draw a circle of radius 3 cm and draw a tangent to the circle from point P on the circle

Q.2 (A)

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 Chapter 4 Geometric Constructions Q.2 (A)

#### Solve the following examples as per the instructions given in the activity [2 Marks]

Q.2 (A) | Q 1
 Draw a circle and take any point P on the circle. Draw ray OP ↓ Draw perpendicular to ray OP from point P
Q.2 (A) | Q 2
 Draw a circle with center O and radius 3 cm ↓ Take any point P on the circle ↓ Draw ray OP ↓ Draw perpendicular to ray OP from point P
Q.2 (A) | Q 3

To draw tangents to the circle from the endpoints of the diameter of the circle.

 Construct a circle with center O. Draw any diameter AB of it ↓ Draw ray OA and ray OB ↓ Construct perpendicular to ray OA from point A ↓ Construct perpendicular to Ray OB from point B
Q.2 (B)

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 Chapter 4 Geometric Constructions Q.2 (B)

#### Solve the following examples [2 Marks]

Q.2 (B) | Q 1

Draw a circle of radius 3.4 cm, take any point P on it. Draw tangent to the circle from point P

Q.2 (B) | Q 2

Draw a circle of radius 4.2 cm, take any point M on it. Draw tangent to the circle from point M

Q.2 (B) | Q 3

Draw a circle of radius 3 cm. Take any point K on it. Draw a tangent to the circle from point K without using center of the circle.

Q.2 (B) | Q 4

Draw a circle of radius 3.4 cm. Draw a chord MN 5.7 cm long in a circle. Draw a tangent to the circle from point M and point N

Q.2 (B) | Q 5

Draw a circle of radius 4.2 cm. Draw a tangent to the circle at point P on the circle without using the center of the circle

Q.2 (B) | Q 6

Draw a circle with a diameter AB of length 6 cm. Draw a tangent to the circle from the end points of the diameter.

Q.2 (B) | Q 7

Draw seg AB = 6.8 cm. Draw a circle with diameter AB. Draw point C on the circle apart from A and B. Draw line AC and line CB. Write the measure of angle ACB

Q.3 (A)

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 Chapter 4 Geometric Constructions Q.3 (A)

#### Do the activity as per the given instructions [3 Marks]

Q.3 (A) | Q 1

Complete the following activity to draw tangents to the circle.

1. Draw a circle with radius 3.3 cm and center O. Draw chord PQ of length 6.6 cm. Draw ray OP and ray OQ.
2. Draw a line perpendicular to the ray OP from P.
3. Draw a line perpendicular to the ray OQ from Q.
Q.3 (A) | Q 2

Draw a circle with center P. Draw an arc AB of 100° measure. Perform the following steps to draw tangents to the circle from points A and B.

1. Draw a circle with any radius and center P.
2. Take any point A on the circle.
3. Draw ray PB such ∠APB = 100°.
4. Draw perpendicular to ray PA from point A.
5. Draw perpendicular to ray PB from point B.
Q.3 (A) | Q 3

Do the following activity to draw tangents to the circle without using the center of the circle.

1. Draw a circle with radius 3.5 cm and take any point C on it.
2. Draw chord CB and an inscribed angle CAB.
3. With the center A and any convenient radius, draw an arc intersecting the sides of angle BAC in points M and N.
4. Using the same radius, draw an arc intersecting the chord CB at point R.
5. Taking the radius equal to d(MN) and center R, draw an arc intersecting the arc drawn in the previous step. Let D be the point of intersection of these arcs. Draw line CD. Line CD is the required tangent to the circle.
Q.3 (B)

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 Chapter 4 Geometric Constructions Q.3 (B)

#### Solve the following examples [3 Marks]

Q.3 (B) | Q 1

∆ABC ~ ∆PBQ. In ∆ABC, AB = 3 cm, ∠B = 90°, BC = 4 cm. Ratio of the corresponding sides of two triangles is 7: 4. Then construct ∆ABC and ∆PBQ

Q.3 (B) | Q 2

ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm, ∠D = 30°, ∠N = 20° and "HP"/"ED" = 4/5. Then construct ΔRHP and ΔNED

Q.3 (B) | Q 3

ΔPQR ~ ΔABC. In ΔPQR, PQ = 3.6cm, QR = 4 cm, PR = 4.2 cm. Ratio of the corresponding sides of triangle is 3 : 4, then construct ΔPQR and ΔABC

Q.3 (B) | Q 4

Construct an equilateral ∆ABC with side 5 cm. ∆ABC ~ ∆LMN, ratio the corresponding sides of triangle is 6 : 7, then construct ΔLMN and ΔABC

Q.3 (B) | Q 5

Draw a circle with center O and radius 3.4. Draw a chord MN of length 5.7 cm in a circle. Draw tangents to the circle from point M and N

Q.3 (B) | Q 6

Draw a circle with center O and radius 3.6 cm. Draw a tangent to the circle from point B at a distance of 7.2 cm from the center of the circle.

Q.3 (B) | Q 7

Draw a circle with center C and radius 3.2 cm. Draw a tangent to the circle from point P at a distance of 7.5 cm from the center of the circle

Q.3 (B) | Q 8

Draw a circle with a radius of 3.5 cm. Take the point K anywhere on the circle. Draw a tangent to the circle from K (without using the center of the circle)

Q.3 (B) | Q 9

Draw a circle of radius 4.2 cm. Draw arc PQ measuring 120°. Draw a tangent to the circle from point P and point Q

Q.3 (B) | Q 10

Draw a circle of radius 4.2 cm. Draw a tangent to the circle from a point 7 cm away from the center of the circle

Q.3 (B) | Q 11

Draw a circle of radius 3 cm and draw chord XY 5 cm long. Draw the tangent of the circle passing through point X and point Y (without using the center of the circle)

Q.4

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 Chapter 4 Geometric Constructions Q.4

#### Solve the following examples [4 Marks]

Q.4 | Q 1

ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, "AM"/"HA" = 7/5, then construct ΔAMT and ΔAHE

Q.4 | Q 2

ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm. ∠D = 30°, ∠N = 20°, "HP"/"ED" = 4/5, then construct ΔRHP and ∆NED

Q.4 | Q 3

ΔABC ~ ΔPBR, BC = 8 cm, AC = 10 cm , ∠B = 90°, "BC"/"BR" = 5/4 then construct ∆ABC and ΔPBR

Q.4 | Q 4

∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm. "AM"/"AH" = 7/5. Construct ∆AHE.

Q.4 | Q 5

Draw a circle with radius 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q. Write your observation about the tangents

Q.4 | Q 6

Draw a circle with center O and radius 3 cm. Take the point P and the point Q at a distance of 7 cm from the center of the circle on the opposite side of the circle such that their line of intersection passing through the center of the circle Draw a tangent to the circle from the point P and the point Q

Q.5

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 Chapter 4 Geometric Constructions Q.5

#### Solve the following examples [3 Marks]

Q.5 | Q 1

Draw a circle with radius 4 cm and construct two tangents to a circle such that when those two tangents intersect each other outside the circle they make an angle of 60° with each other

Q.5 | Q 2

AB = 6 cm, ∠BAQ = 50°. Draw a circle passing through A and B so that AQ is the tangent to the circle

Q.5 | Q 3

Draw a circle with radius 3 cm. Construct a square such that each of its side will touch the circle from outside

Q.5 | Q 4

Take point P and Q and draw a circle passing through them. Draw a tangent AB to the circle without using the centre of the circle.

Q.5 | Q 5

Draw any circle with radius greater than 1.8 cm and less than 3 cm. Draw a chord AB 3.6 cm long in this circle. Tangent to the circle passing through A and B without using the center of the circle

Q.5 | Q 6

Draw a circle with center O and radius 3 cm. Take point P outside the circle such that d (O, P) = 4.5 cm. Draw tangents to the circle from point P.

Q.5 | Q 7

Draw a circle with center O and radius 2.8 cm. Take point P in the exterior of a circle such that tangents PA and PB drawn from point P make an angle ∠APB of measure 70°

Q.5 | Q 8

Point P is at a distance of 6 cm from line AB. Draw a circle of radius 4 cm passing through point P so that line AB is the tangent to the circle

## Chapter 4: Geometric Constructions

Q.1 (A)Q.1 (B)Q.2 (A)Q.2 (B)Q.3 (A)Q.3 (B)Q.4Q.5

## SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 chapter 4 - Geometric Constructions

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Concepts covered in 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 chapter 4 Geometric Constructions are To Construct Tangents to a Circle from a Point Outside the Circle., Basic Geometric Constructions, Division of a Line Segment, Construction of Similar Triangle, Construction of a Tangent to the Circle at a Point on the Circle.

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