ML Aggarwal Constructions Ch-Test Class 10 ICSE Maths Solutions Ch-16. We Provide Step by Step Answer of Ch-Test 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 Ch-Test Class 10 ICSE Maths Solutions

Board | ICSE |

Subject | Maths |

Class | 10th |

Chapter-16 | Constructions |

Writer / Book | Understanding |

Topics | Solutions of Ch-Test |

Academic Session | 2024-2025 |

### Constructions Ch-Test Questions

ML Aggarwal Class 10 ICSE Maths Solutions Ch-16

(Page 388)

**Question 1. **Draw a circle of radius 3 cm. Mark its centre as C and mark a point P such that CP = 7 cm. Using ruler and compasses only, Construct two tangents from P to the circle.

**Answer 1 ****Steps of Construction :**

- Draw a circle with centre C and radius 3 cm.
- Mark a point P such that CP = 7 cm.
- With CP as diameter, draw a circle intersecting the given circle at T and S.
- Join PT and PS.
- Draw a tangent at Q to the circle given. Which intersects PT at D.
- Draw the angle bisector of ∠PDQ intersecting CP at E.
- With centre E and radius EQ, draw a circle.

It will touch the tangent T and PS and the given circle at Q.

This is the required circle.

**Question 2. **Draw a line AQ = 7 cm. Mark a point P on AQ such that AP = 4 cm. Using ruler and compasses only, construct :

(i) a circle with AP as diameter.

(ii) two tangents to the above circle from the point Q.

**Answer 2 **Steps of construction :

- Draw a line segment AQ = 7 cm.
- From AQ, cut off AP = 4cm
- With AP as diameter draw a circle with centre O.
- Draw bisector of OQ which intersect OQ at M.
- With centre M and draw a circle with radius MQ

which intersects the first circle at T and S. - Join QT and QS.

QT and QS are the tangents to the first circle.

**Question 3. **Using ruler and compasses only, construct a triangle ABC having given c = 6 cm, b = 7 cm and ∠A = 30°. Measure side a. Draw carefully the circumcircle of the triangle.

**Answer 3 ****Steps of Construction :**

- Draw a line segment AC = 7 cm.
- At C, draw a ray CX making an angle of 30°
- With centre A and radius 6 cm draw an arc

which intersects the ray CX at B. - Join BA.
- Draw perpendicular bisectors of AB and AC intersecting each other at O.
- With centre O and radius OA or OB or OC,

draw a circle which will pass through A, B and C.

This is the required circumcircle of ∆ABC

**Question 4. **Using ruler and compasses only, construct an equilateral triangle of height 4 cm and draw its circumcircle.

**Answer 4 ****Steps of Construction :**

- Draw a line XY and take a point D on it.
- At D, draw perpendicular and cut off DA = 4 cm.
- From A, draw rays making an angle of 30°

on each side of AD meeting the line XY at B and C. - Now draw perpendicular bisector of AC intersecting AD at O.
- With centre O and radius OA or OB or OC

draw a circle which will pass through A, B and C.

This is the required circumcircle of ∆ABC.

**Question 5. **Using ruler and compasses only :

(i) Construct a triangle ABC with the following data: BC = 7 cm, AB = 5 cm and ∠ABC = 45°.

(ii) Draw the inscribed circle to ∆ABC drawn in part (i).

**Answer 5 ****Steps of construction :**

- Draw a line segment BC = 7 cm.
- At B, draw a ray BX making an angle of 45° and cut off BA = 5 cm.
- Join AC.
- Draw the angle bisectors of ∠B and ∠C intersecting each other at I.
- From I, draw a perpendicular ID on BC.
- With centre, I and radius ID, draw a circle

which touches the sides of ∆ABC at D, E and F respectively.

This is the required inscribed circle.

### ML Aggarwal Constructions Ch-Test Class 10 ICSE Maths Solutions Ch-16.

**Question 6. **Draw a triangle ABC, given that BC = 4cm, ∠C = 75° and that radius of the circumcircle of ∆ABC is 3 cm.

**Answer 6 ****Steps of Construction:**

- Draw a line segment BC = 4 cm
- Draw the perpendicular bisector of BC.
- From B draw an arc of 3 cm radius which intersects the perpendicular bisector at O.
- Draw a ray CX making art angle of 75°
- With centre O and radius 3 cm draw a circle which intersects the ray CX at A.
- Join AB.

∆ABC is the required triangle

**Question 7. **Draw a regular hexagon of side 3.5 cm construct its circumcircle and measure its radius.

**Answer 7 ****Steps of construction:**

- Draw a regular hexagon ABCDEF whose each side is 3.5 cm.
- Draw the perpendicular bisector of AB and BC

which intersect each other at O. - Join OA and OB.
- With centre O and radius OA or OB, draw a circle

which passes through A, B, C, D, E and P.

Then this is the required circumcircle.

**Question 8. **Construct a triangle ABC with the following data:

AB = 5 cm, BC = 6 cm and ∠ABC = 90°.

(i) Find a point P which is equidistant from B and C and is 5 cm from A. How many such points are there ?

(ii) Construct the inscribed circle of triangle ABC drawn above.

**Answer 8 ****Steps of Construction :**

- Draw a line segment BC = 6 cm.
- At B, draw a ray BX making an angle of 90° and cut off BA = 5 cm.
- Join AC.
- Draw the perpendicular bisector of BC.
- From A with 5 cm radius draw arc which intersects the perpendicular bisector of BC at P and P’.

There are two points. - Draw the angle bisectors of ∠B and ∠C intersecting at 0.
- From O, draw OD ⊥ BC.
- With centre O and radius OD, draw a circle which will touch the sides AB and BC.

This is the required circle.

— : End of ML Aggarwal Constructions Ch-Test Class 10 ICSE Maths Solutions Ch-16 :–

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

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