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Question

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

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Solution

Step 1: Draw a line segment PQ=6.5 cm

Step 2: With P and Q as centres, draw arc with radii 7 cm and 5.5 cm respectively, to intersect at R. Join PR and QR.

Step 3: Draw the perpendicular bisectors of PQ and QR intersect at O.

Step 4: With O as centre and OP(=OQ=OR) as radius, draw the circumcircle of PQR.

Step 5 With P as centre and radius 4.5 cm, draw an arc intersecting the circle at S.

Step 6: Join PS and RS.

Step 8: PQRS is the required cyclic quadrilateral.

Hence, this is the answer.

1373011_622505_ans_6643c29b40df418db68d74e0d1fc149a.jpg

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