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Question
Using ruler and compass only, construct a ΔABC such that BC = 5 cm and AB = 6.5
cm and ∠ABC = 120°
1) Construct a circum-circle of ΔABC
2) Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC.
Solution
Steps of construction:
1) Draw a line segment BC of length 5 cm.
2) At B, draw a ray BX making an angle of 120° with BC.
3) With B as centre and radius 6.5 cm, draw an arc to cut the ray BX at A. Join AC.
ΔABC will be obtained
4) Draw the perpendicular bisectors of AB and BC to meet at point O.
5) With O as centre and radius OA, draw a circle. The circle will circumscribe ΔABC
6) Draw the angle bisector of ∠ABC
7) The angle bisector of ABC and let it meet circle at point D.
8) Join AD and DC to obtain the required cyclic quadrilateral ABCD such that point D is equidistant from AB and BC.
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