मराठी

Using a Ruler and Compass Only: (I) Construct a Triangle Abc with Bc = 6 Cm, ∠Abc = 120° and Ab = 3.5 Cm. (Ii) in the Above Figure, Draw a Circle with Bc as Diameter. Find a Point 'P' on the - Mathematics

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प्रश्न

Using a ruler and compass only: 
(i) Construct a triangle ABC with BC = 6 cm, ∠ABC = 120° and AB = 3.5 cm.
(ii) In the above figure, draw a circle with BC as diameter. Find a point 'P' on the circumference of the circle which is equidistant from Ab and BC.
Measure ∠BCP.

आकृती
बेरीज

उत्तर

(i) Steps of  construction:
(1) Draw BC = 6 cm.
(2) Draw ∠ABC = 120°.
(3) Cut BA = 3·5 cm.
(4) Join A to C.
(5) Draw ⊥ bisector MN of BC.
(6) Draw a circle O as centre and OC, OB radius.
(7) Draw angle bisector of ∠ABC which intersect circle at P.

(ii) ∠BCP = 30°.

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पाठ 14: Loci (Locus and its Constructions) - Figure Based Questions

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आईसीएसई Mathematics [English] Class 10
पाठ 14 Loci (Locus and its Constructions)
Figure Based Questions | Q 11

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Describe the locus of vertices of all isosceles triangles having a common base.


Describe the locus of a point in space, which is always at a distance of 4 cm from a fixed point.  


Construct a triangle BCP given BC = 5 cm, BP = 4 cm and ∠PBC = 45°.

  1. Complete the rectangle ABCD such that:
    1. P is equidistant from AB and BC.
    2. P is equidistant from C and D.
  2. Measure and record the length of AB. 

Describe completely the locus of point in  the following cases: 

Midpoint of radii of a circle. 


Describe completely the locus of points in the following cases: 

Centre of a circle of varying radius and touching the two arms of ∠ ABC. 


State and draw the locus of a swimmer maintaining the same distance from a lighthouse.


Using ruler and compasses construct:
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of point equidistant from A and C.
(iii) a circle touching AB at A and passing through C.


Ruler and compass only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct Δ ABC, in which BC = 8 cm, AB = 5 cm, ∠ ABC = 60°.
(ii) Construct the locus of point inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark as P, the point which is equidistant from AB, BC and also equidistant from B and C.
(v) Measure and record the length of PB.


Ruler and compasses only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct a ΔABC, in which BC = 6 cm, AB = 9 cm and ∠ABC = 60°.
(ii) Construct the locus of the vertices of the triangles with BC as base, which are equal in area to ΔABC.
(iii) Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
(iv) Measure and record the length of CQ.


Given ∠BAC (Fig), determine the locus of a point which lies in the interior of ∠BAC and equidistant from two lines AB and AC.


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