Mathematics
Angle ABC = 60° and BA = BC = 8 cm. The mid points of BA and BC are M and N respectively. Draw and describe the locus of a point which is :
(i) Equidistant from BA and BC.
(ii) 4 cm from M
(iii) 4 cm from N
Mark the point P, which is 4 cm from both M and N, and equidistant from BA and BC. Join MP and NP, and describe the figure BMPN.
Locus
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Answer
Steps of construction :
Draw BC = 8 cm.
Draw ∠XBC = 60°.
From XB, cut off AB = 8 cm. Join AC.
Mark mid-point of BA as M and BC as N.
Draw angle bisector of ∠ABC.
Taking center as M and radius = 4 cm draw a circle.
Taking center as N and radius = 4 cm draw a circle.
Mark point P as the intersection of circle with center M, N and angle bisector of ∠ABC.
Join MP and NP.
From figure,
BMPN is a rhombus.
(i) Hence, the locus of points equidistant from BA and BC is the bisector of ∠ABC.
(ii) Hence, the locus of point at a distance of 4 cm from M is the circumference of the circle with center M and radius = 4 cm.
(iii) Hence, the locus of point at a distance of 4 cm from N is the circumference of the circle with center N as radius = 4 cm.
Figure BMPN is a rhombus
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