Construct a cyclic quadrilateral PQRS given PQ = 5 cm, QR = 4 cm, ∠QPR = 35° and ∠PRS = 70°

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.