Answer :

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 line segment PQ = 5 cm.



Step 2: Through P draw PX such that QPX = 35°



Step 3: With Q as centre and radius 4 cm, draw an arc intersecting PX at R and join QR..



Step 4: Draw the perpendicular bisectors of PQ and QR intersecting each other at O.



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



Step 6: From R, draw RY such that PRS = 70° , which intersects the circle at S.



Step 7: Join PS.



Thus, PQRS is required cyclic quadrilateral.


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