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Use ruler and compass only for this question construct the cyclic quadrilateral ABCD in which AB = 5 cm, BC = 8 cm, ABC = 67.1/2˚ and D is equidistant from B and C.

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Steps of Construction :

(1) Draw BC = 8 cm, construct B = 67.1/2˚ and cut off AB = 5 cm.

(2) Draw bisector of BC and AB and produce these to meet at O.

(3) With O as centre, radius OA or OB or OC draw a circle to pass through ABC.

(4) Produce the bisector of BC to intersect the circumference of the circle. This intersection point is D.

(5) Join CD and AD.

(6) ABCD is the required cyclic quadrilateral. Length of CD = 6.4 cm (By measurement)

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