# 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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