Construct a cyclic quadrilateral ABCD in which AB $= 6$ cm, AC $= 7$ cm, BC $= 6$ cm, and AD $= 4.2$ cm.

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Solution

Given: In the cyclic quadrilateral ABCD, AB $= 6$ cm, AC $= 7$ cm, BC $= 6$ cm, and AD $= 4.2$ cm.
Construction:
(i) Draw a rough diagram and mark the measurements.
(ii) With A and B as centres, draw arcs with radii $7$ cm and $6$ cm respectively, to intersect at C. Join AC and BC.
(iii) Draw the perpendicular bisectors of AB and BC to intersect at O.
(iv) With O as the centre and OA $(= O B = O C)$ as radius draw the circumcircle of $Δ$ ABC.
(v) With A as the centre and radius $4.2$ cm. Draw an arc intersecting the circumcircle at D.
(vi) Join AD and CD.
Now, ABCD is the required cyclic quadrilateral.

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Question 1
Construct the Quadrilateral ABCD where
AB=4.5 cm, BC=5.5 cm, CD=4 cm,AD=6cm, AC=7 cm

In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?

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Construct a cyclic quadrilateral ABCD in which AB=6cm, AC=7cm, BC=6cm, and AD=4.2cm.

Construct a cyclic quadrilateral ABCD in which AB $= 6$ cm, AC $= 7$ cm, BC $= 6$ cm, and AD $= 4.2$ cm.