Mathematics
Without using set square or protractor construct :
(i) Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
(ii) Draw the locus of a point which moves so that it is always 2.5 cm from B.
(iii) Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
(iv) Mark the point of intersection of the loci with the letter P and measure PC.
Locus
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Answer
(i) Steps of Construction :
Draw BC = 3.2 cm as base.
From B cut an arc of of 5.5 cm and from C cut an arc of 4.8 cm. Take their intersection as point A.
Join the points to form triangle ABC.
(ii) The locus of point that is always 2.5 cm from point B will be a circle with center as B and radius 2.5 cm.
(iii) We know that locus of points equidistant from two lines is the angle bisector of angle between them.
From figure,
CD is the angular bisectors of ACB, hence it will be equidistant from CA and BC.
(iv) There are two points P1 and P2 which intersect the circle.
On measuring we get,
P1C = 1.1 cm and P2C = 3.6 cm.
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