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Without Using Set Squares Or Protractor. (I) Construct a δAbc, Given Bc = 4 Cm, Angle B = 75° and Ca = 6 Cm. (Ii) Find the Point P Such that Pb = Pc and P is Equidistant from the Side Bc and Ba. - Mathematics

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प्रश्न

Without using set squares or protractor.
(i) Construct a ΔABC, given BC = 4 cm, angle B = 75° and CA = 6 cm.
(ii) Find the point P such that PB = PC and P is equidistant from the side BC and BA. Measure AP.

आकृति
योग

उत्तर

(i) Draw BC = 4 cm. Draw BA at B such that ∠ABC = 75°. Cut  CA = 6 cm. Then ΔABC is the required Δ.

(ii) Draw single bisector of ∠B. Draw ⊥ bisector of BC. Their point of intersection (P) is the requisite point.
AP = 3·9 cm.

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

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आईसीएसई Mathematics [English] Class 10
अध्याय 14 Loci (Locus and its Constructions)
Figure Based Questions | Q 24

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संबंधित प्रश्न

Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105°

Hence:

1) Construct the locus of points equidistant from BA and BC

2) Construct the locus of points equidistant from B and C.

3) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.


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AB and CD are two intersecting lines. Find a point equidistant from AB and CD, and also at a distance of 1.8 cm from another given line EF. 


Construct a rhombus ABCD with sides of length 5 cm and diagonal AC of length 6 cm. Measure ∠ ABC. Find the point R on AD such that RB = RC. Measure the length of AR. 


Describe completely the locus of points in the following cases: 

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Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.

  1. Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
  2. Construct the locus of points at a distance of 3.5 cm from A.
  3. Construct the locus of points equidistant from AC and BC.
  4. Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.

Using only a ruler and compass construct ∠ABC = 120°, where AB = BC = 5 cm.
(i) Mark two points D and E which satisfy the condition that they are equidistant from both ABA and BC.
(ii) In the above figure, join AD, DC, AE and EC. Describe the figures:
(a) AECB, (b) ABD, (c) ABE.


How will you find a point equidistant from three given points A, B, C which are not in the same straight line?


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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