Construct a cyclic quadrilateralABCDin whichAB= 3.5 cm,BC= 6 cm,CA= 4 cm andAD= 2.2 cm. Also construct a quadrilateral s

Solution

Given: Three sides and a diagonal of a cyclic quadrilateral ABCD in which AB = 3.5 cm, BC = 6 cm, and AD = 2.2 cm and diagonal AC = 4 cm.

Required: To construct the cycle quadrilateral ABCD and another quadrilateral similar quadrilateral ABCD whose sides are 1.5 times the corresponding sides of ABCD, i.e. quadrilateral in which = 1.5 AB, = 1.5 BC, = 1.5 CD and A = 1.5 DA

Steps of Construction:

1. Draw the line segment AC = 4 cm.

2. With centre A and radius equal to 3.5 cm, draw an arc.

3. With centre C and radius equal to 6 cm, draw another arc cutting the previous arc at B.

4. Join BA and BC.

5. Draw PQ and RS the perpendicular bisectors of any two sides, say AC and BC respectively of ∠ABC intersecting of O.

6. With O as centre and radius equal to OA (or OB or OC), draw a circle. This circle is the circumcircle of ∠ABC.

7. With centre A and radius equal to 2.2 cm, draw an arc on the opposite side of point B, to cut the circle at point D.

8. Join AD and CD.

Then ABCD is the required cyclic quadrilateral.

9. Draw ant ray AX inclined at a certain acute angle with AC on the opposite side of B.

10. Starting from A, cut off three equal line segments and on .

11. Join and draw a line segment parallel to to intersect AC produced at .

12. Draw a line parallel to CB which intersects AB produced at B’.

13. Draw a line parallel to CB which intersects AD produced at D’.

Then quadrilateral is the required quadrilateral similar to cyclic quadrilateral ABCD.