Mathematics
Using ruler and compasses only, construct a △ABC such that BC = 5 cm, AB = 6.5 cm and ∠ABC = 120°.
(i) Construct a circumcircle of △ABC.
(ii) Construct a cyclic quadrilateral ABCD such that D is equidistant from AB and BC.
Constructions
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Answer
(i) Steps of construction :
Draw a line segment AB = 6.5 cm.
From B construct angle 120° and extend the line such that BC = 5 cm.
Join points A, B and C. Hence, the △ABC is formed.
Draw the perpendicular bisector of AB and BC. Let these bisectors meet at the point O.
With O as center and radius equal to OA, draw a circle. The circle so drawn passes through the points A, B and C, and is required circumcircle of △ABC.
(ii) We know that locus of point equidistant from two sides is the angle bisector of the angle between the lines.
Steps of construction :
Draw the angle bisector of ∠ABC.
Mark the point as D where the angle bisector of ∠ABC meets the circumcircle.
Join AD and CD.
ABCD is the cyclic quadrilateral.
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