Mathematics
Using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6 cm, BC = 5 cm, ∠B = 60°, AD = 5 cm and D is equidistant from AB and BC.
Answer
Steps of construction :
Draw BC = 5 cm as base.
Make angle 60° at B.
Cut off an arc of 6 cm from B at the angle and mark it A as in figure.
Since, D is equidistant from AB and BC hence, it will lie on angle bisector of ∠ABC i.e. on BE.
Make an arc of 5 cm from point A take point D where the arc cuts BE.
Join, the points A, B, C and D to form quadrilateral ABCD.
Related Questions
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.
Using ruler and compasses only, construct an isosceles ΔABC in which BC = 5 cm, AB = AC and ∠BAC = 90°. Locate the point P such that :
(i) P is equidistant from BC and AC.
(ii) P is equidistant from B and C.
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.