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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