मराठी

Construct a Triangle Abc, Such that Ab= 6 Cm, Bc= 7.3 Cm and Ca= 5.2 Cm. Locate a Point Which is Equidistant from A, B and C.

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प्रश्न

Construct a triangle ABC, such that AB= 6 cm, BC= 7.3 cm and CA= 5.2 cm. Locate a point which is equidistant from A, B and C.

आकृती
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उत्तर

Steps of construction: 

(i) Draw a line segment BC= 7.3 cm. 

(ii) With Bas centre and radius 6 cm draw an arc. 

(iii) With C as centre and radius 5.2 cm draw another arc which intersects the first arc at A. 

(iv) Join AB and AC. 

(v) Draw perpendicuIar bisector of BC , AB and AC. 
In triangIe ABC, P is the point of intersection of AB , AC and BC. 

Therefore, PA = PB, PB = PC, PC = PA. 

Thus, circum-centre of a triangle is the point which is equidistant from all its vertices. 

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पाठ 15: Loci - Exercise 16.1

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Construct a triangle ABC, with AB = 6 cm, AC = BC = 9 cm. Find a point 4 cm from A and equidistant from B and C. 


Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB. 


Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6 cm, BC= 3.6 cm and CD=5 cm. Locate the point P on BD which is equidistant from BC and CD. 


Draw and describe the locus in the following case:

The locus of a point in rhombus ABCD which is equidistant from AB and AD.


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

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  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.

Without using set squares or protractor construct a triangle ABC in which AB = 4 cm, BC = 5 cm and ∠ABC = 120°.
(i) Locate the point P such that ∠BAp = 90° and BP = CP.
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(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.


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.


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