Q1 of 20 Page 266

Construct a cyclic quadrilateral PQRS, with PQ = 6.5 cm, QR = 5.5 cm, PR = 7cm and PS = 4.5 cm.

We need to construct the required quadrilateral, when three sides and one diagonal of a cyclic quadrilateral are given.


Steps of construction:


Step 1: Draw a rough diagram and mark the measurements



Step 2: Draw a line segment PQ = 6.5 cm.



Step 3: With P and Q as centres, draw arc with radii 7 cm and 5.5cm respectively, to intersect at R. join PR and QR.



Step 4: Draw the perpendicular bisectors of PQ and QR to intersect at O.



Step 5: With O as the centre and OP (=OQ = OR ) as radius draw the circumcircle of Δ PQR



Step 6: With P as the centre and radius 4.5 cm draw an arc intersecting the circumcircle at S.



Step 7: Join PS and RS.



Step 8: PQRS is the required cyclic quadrilateral.



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Construct a cyclic quadrilateral ABCD where AB = 6 cm, AD = 4.8 cm, BD = 8 cm and CD = 5.5 cm.

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