Mathematics
Using ruler and compasses only, construct a ΔABC in which AB = 6 cm, BC = 3.5 cm and CA = 4.6 cm.
(i) Draw the locus of a point P which moves so that it is always 3 cm from B.
(ii) Draw the locus of a point which moves so that it is equidistant from BC and CA.
(iii) Mark the point of intersection of the two loci obtained above. Measure PC.
Answer
Steps of construction :
Draw a line segment AB = 6 cm.
With B as the center and a radius of 3.5 cm, draw an arc.
With A as the center and a radius of 4.6 cm, draw a second arc intersecting the first arc at C.
Join ABC, ABC is required triangle.
With B as the center and a radius of 3 cm, draw a circle.
Draw the angle bisector of C.
Mark the point where bisector meets circle as P and P'. Measure CP and CP'.
On measuring PC = 4 cm and CP' = 1.5 cm.
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