NCERT Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.2 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 11 Constructions** Class 10 NCERT Solutions Ex 11.2.**

Board | CBSE |

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 11 |

Chapter Name | Constructions |

Exercise | Ex 11.2 |

Number of Questions Solved | 7 |

Category | NCERT Solutions |

## NCERT Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.2

NCERT Solutions for Class 10 Maths

Page No. 221

**Question 1.** 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.

**Solution: **The steps of construction are as follows:

1. Taking any point O of the given plane as centre draw a circle of 6 cm. radius. Locate a point P, 10 cm away from O. Join OP.

2. Bisect OP. Let M be the midpoint of PO,

3. Taking M as centre and MO as radius draw a circle.

4. Let this circle intersect our circle at point Q and R.

5. Join PQ and PR. PQ and PR are the required tangents.

The length of tangents PQ and PR are 8 cm each.

**Question 2.** Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

**Solution: **The steps of construction are as follows:

1. Draw a circle of 4 cm radius with centre as O on the given plane.

2. Draw a circle of 6 cm radius taking O as its centre. Locate a point P on this circle and join OP.

3. Bisect OP. Let M be the midpoint of PO.

4. Taking M as its centre and MO as its radius draw a circle. Let it intersects the given circle at the points Q and R.

5. Join PQ and PR. PQ and PR are the required tangents.

Now, PQ and PR are of length 4.47 cm each.

In ∆PQO, since PQ is tangent, ∠PQO = 90°.

PO = 6 cm

QO=4cm

Applying Pythagoras theorem in ∆PQO,

PQ

^{2}+ QO

^{2}= PQ

^{2}

PQ

^{2}+ (4)

^{2}= (5)

^{2}

PQ

^{2}= 20

PQ =2√5= 4.47 cm

**Question 3.** Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

**Solution: **The steps of construction are as follows:

1. Taking any point O on given plane as centre draw a circle of 3 cm radius.

2. Take one of its diameters, PQ, extend it on both sides. Locate two points on this diameter such that OR = OS = 7 cm.

3. Bisect OR and OS. Let T and U be the midpoints of OR and OS respectively.

4. Taking T and U as its centre, with TO and UO as radius draw two circles. These two circles will intersect our circle at point V, W, X, Y respectively. Join RV, RW, SX, and SY. These are required tangents.

**Question 4.** Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

**Solution: **

**Question 5.** Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

**Solution: **The steps of construction are as follows:

1. Draw a line segment AB of 8 cm. Taking A and B as centre draw two circles of 4 cm and 3 cm radius.

2. Bisect the line AB. Let midpoint of AB is C. Taking C as centre draw a circle of AC radius which will intersect our circles at point P, Q, R and S. Join BP, BQ, AS and AR.These are our required tangents.

**Question 6.** Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

**Solution: **In the following figure, it can be seen that if a circle is drawn through B, D and C, then BC will be its diameter as ∠BDC is of 90°, The centre E of this circle will be the midpoint of BC.

The steps of construction are as follows:

1. Join AE and bisect it. Let F be the midpoint of the AE.

2. Now taking F as centre and FE as its radius draw a circle which will intersect our circle at point B and G. Join AG.

AB and AG are the required tangents.

**Question 7.** Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circles.

**Solution: **The steps of construction are as follows:

1. Draw a circle, with the help of bangle.

2. Take a point P outside this circle and take two chords QR and ST.

3. Draw perpendicular bisectors of these chords. Let they intersect each other at point O.

4. Join PO and bisect it. Let U be the midpoint of PO. Taking U as centre, draw a circle of radius OU, which will intersect our circle at V and W. Join PV and PW.

PV and PW are required tangents.

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