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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