Mathematics
Use ruler and compass for the following constructions:
Construct:
(a) an isosceles ΔABC in which AB = AC = 7 cm and BC = 6 cm.
(b) the locus of points which moves such that it is 2.5 cm from the point A.
(c) the locus of points equidistant from B and C. Mark point P which satisfies both the conditions mentioned in (b) and (c).
(d) a circle passing through P, B and C.
Constructions
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Answer
We know that,
The locus of points at a fixed distance from a point, is the circle with fixed point as center and distance as radius.
The locus of points equidistant from two points is the perpendicular bisector of the line joining the two points.
Steps of Construction:
Draw a line segment BC of length 6 cm.
Take point B as the center, use a compass to draw an arc with a radius of 7 cm. With C as the center and radius 7 cm draw another arc that intersects the first arc. Label the point of intersection as A. Join A to B and A to C to form the isosceles triangle ABC.
With A as center and radius 2.5 cm draw a circle.
Construct the perpendicular bisector of the line BC. Mark one of the points where the circle and the perpendicular bisector intersect as P.Join PB and PC.
Draw the perpendicular bisector of PB and PC.
Mark the point as O, where the perpendicular bisectors of PB, BC and PC meet.
With O as center and radius equal to OB draw a circle passing through the points P, B and C.
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