ML Aggarwal Constructions Exe-16.1 Class 10 ICSE Maths Solutions. We Provide Step by Step Answer of Exe-16.1 Questions for Constructions as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-10.

## ML Aggarwal Constructions Exe-16.1 Class 10 ICSE Maths Solutions

Board | ICSE |

Subject | Maths |

Class | 10th |

Chapter-16 | Constructions |

Writer / Book | Understanding |

Topics | Solutions of Exe-16.1 |

Academic Session | 2024-2025 |

**Constructions Exe-16.1**

ML Aggarwal Class 10 ICSE Maths Solutions

(Page 381)

**Question 1. Use a ruler and compass only in this question.**

(i) Draw a circle, centre O and radius 4 cm.

(ii) Mark a point P such that OP = 7 cm.

Construct the two tangents to the circle from P. Measure and record the length of one of the tangents.

**Answer :**

**Steps of Construction:**

- Draw a circle with centre O and radius 4 cm.
- Take a point P such that OP = 7 cm.
- Bisect OB at M.
- With centre M and diameter OP,

draw another circle intersecting the given circle at A and B. - Join PA and PB.

PA and PB is a pair of tangents to the circle. - On measuring PA, it is equal to 5.5 cm.

**Question 2. **Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent

**Answer :**

**Steps of Construction:**

- Take a line segment AB = 6 cm.
- Draw its perpendicular bisector bisecting it at O.
- With centre O and radius OB, draw a circle.
- Produce AB to P such that OP = 5 cm.
- Draw its perpendicular bisector intersecting it at M.
- With centre M and radius OM, draw a circle

which intersects the given circle at T and S. - Join OT, OS, TP and SP.

PT and PS are the required tangents to the given circle. - On measuring, each tangent is 4 cm long i.e. PT = PS = 4 cm.

**Question 3. **Construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.

**Answer :**

**Steps of construction:**

- Take a point O.
- With centre O and radii 4 cm and 6 cm, draw two concentric circles.
- Join OA and take its mid-point M.
- With centre M and radius MA, draw another circle

which intersects the first circle at P and Q. - Join AP and AQ.

AP and AQ are the required tangents to the first circle from point A.

**Question 4. **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.

**Answer :**

**Steps of construction:**

- Take a point O and with centre O, and radius 3 cm, draw a circle.
- Produce its diameter both sides and cut off OP = OQ = 7 cm.
- Take mid-points of OP and OQ as M and N respectively.
- With centers M and N and OP and OQ as diameters,

draw circles which intersect the given circle at A, B and C and D respectively. - Join PA, PB, QC and QD.

PA, PB and QC and QD are the required tangents.

— : End of ML Aggarwal Constructions Exe-16.1 Class 10 ICSE Maths Solutions :–

Return to :- ML Aggarwal Solutions for ICSE Class-10

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