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. Measure CD.
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.
Make an arc of 5 cm from point A take point D where the arc cuts angle bisector BE.
Join, the points A, B, C and D to form quadrilateral ABCD.
On measuring we get, CD = 5.25 approximately.
Related Questions
Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.
Use ruler and compasses only for this question. 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. Prove your construction.
(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.
By using ruler and compasses only, construct an isosceles triangle ABC in which BC = 5 cm, AB = AC and ∠BAC = 90°. Locate the point P such that
(i) P is equidistant from the sides BC and AC.
(ii) P is equidistant from the points B and C.
Using ruler and compass only, construct a semicircle with diameter BC = 7 cm. Locate a point P on the circumference of the semicircle such that A is equidistant from B and C. Completely the cyclic quadrilateral ABCD such that D is equidistant from AB and BC. Measure ∠ADC and write it down.