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Construct a cyclic quadrilateral ABCD in...

Construct a cyclic quadrilateral ABCD in which AB=4.2 cm, BC=5.5 cm, CA=4.6 cm and AD=3 cm. Also construct a quadrilatral similar to `squareABCD` whose side are 1.5 times the corresponding sides of `squareABCD`.

Text Solution

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Steps of construction :
1. Draw a line segment AB=4.2 cm.
2. With centre A and radius equals to 4.6 cm, draw an arc.
3. With centre B and radius equals to 5.5 cm, draw another arc cutting the previous arc at C.
4. Join AC and BC.
5. Draw the perpendicular bisectors of any two sides say AB and BC respectively of `DeltaABC`. Let they intersect each other at O.
6. Taking O as centre and radius as OA or OB or OC, draw a circle.
This is the circumcircle of `DeltaABC`.
7. With centre A and radius equals to 3 cm, cut an arc on the opposite side of B, to cut the circle at D.
8. Join AD and CD.
Then, `squareABCD` is the required cyclic quadrilateral.
9. Produce AC to C' such that AC'`=1.5xxAC` i.e., `(1+(1)/(2)) AC implies AC +(1)/(2)xx4.6` i.e., 2.3 cm more.
10. From C', draw a line parallel to CD which meets AD produced at D'.
11. From C', draw a line parallel to CB which meets AB produced at B'.
Then `, squareAB'C'D'` is the required quadrilateral similar to cyclic quadrilateral ABCD.
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