Mathematics
A and B are fixed points 5 cm apart. The locus of the point P is the set of those points for which AP = 4 cm and the locus of Q is the set of those points for which BQ = 3.5 cm.
Construct the loci of P and Q and the points of intersection of the two loci. How many such points are there?
Answer
Steps of construction :
Draw a line segment AB = 5 cm.
With A as the center and a radius of 4 cm, draw the circle.
With B as the center and a radius of 3.5 cm, draw the circle.
Mark the two points where the circle intersect as P and Q.
The loci of point P is a circle with center as point A and loci of point Q is a circle with centre as point B.
The two circles intersect at two distinct points.
Related Questions
Using ruler and compasses only, construct a parallelogram ABCD in which AB = 5.1 cm, diagonal AC = 5.6 cm and diagonal BD = 7 cm. Locate the point P on DC, which is equidistant from AB and BC.
Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of length 6 cm and 5 cm respectively.
(i) Construct the locus of points inside the circle, that are equidistant from A and C.
(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.
Using only a ruler and compasses, construct ∠ABC = 120°, where AB = BC = 5 cm.
(a) Mark two points D and E which satisfy the condition that they are equidistant from both BA and BC.
(b) In the above figure, join AE and EC. Describe the figures.
(i) ABCD
(ii) BD
(iii) ABEUsing ruler and compasses only,
(i) Construct a ΔABC in which BC = 6 cm, ∠ABC = 120° and AB = 3.5 cm.
(ii) In the above figure, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC. Measure ∠BCP.