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.
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