#### Chapters

Chapter 2: Pythagoras Theorem

Chapter 3: Circle

Chapter 4: Geometric Constructions

Chapter 5: Co-ordinate Geometry

Chapter 6: Trigonometry

## Chapter 4: Geometric Constructions

### 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]

**Choose the correct alternative:**

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

3

2

1

0

**Choose the correct alternative:**

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

Perpendicular

parallel

congruent

can’t say

**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

**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

**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`

**Choose the correct alternative:**

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

Tangent – radius theorem

Converse of tangent – radius theorem

Pythagoras theorem

Converse of Pythagoras theorem

**Choose the correct alternative:**

ΔPQR ~ ΔABC, `"PR"/"AC" = 5/7`, then

ΔABC is greater

ΔPQR is greater

Both triangles are congruent

Can’t say

**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

### 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]

Construct ∠ABC = 60° and bisect it

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

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.

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

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

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

### 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]

Draw a circle and take any point P on the circle. Draw ray OP |

↓ |

Draw perpendicular to ray OP from point P |

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 |

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 |

### 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]

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

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

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.

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

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

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

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

### 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]

Complete the following activity to draw tangents to the circle.

- 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.
- Draw a line perpendicular to the ray OP from P.
- Draw a line perpendicular to the ray OQ from Q.

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.

- Draw a circle with any radius and center P.
- Take any point A on the circle.
- Draw ray PB such ∠APB = 100°.
- Draw perpendicular to ray PA from point A.
- Draw perpendicular to ray PB from point B.

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

- Draw a circle with radius 3.5 cm and take any point C on it.
- Draw chord CB and an inscribed angle CAB.
- With the center A and any convenient radius, draw an arc intersecting the sides of angle BAC in points M and N.
- Using the same radius, draw an arc intersecting the chord CB at point R.
- 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.

### 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]

∆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

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

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

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

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

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.

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

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)

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

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

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)

### 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]

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

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

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

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

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

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

### 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]

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

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

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

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.

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

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.

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°

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

## 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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