Question

Construct a cyclic quadrilateral PQRS with PQ = 4 cm, QR = 6 cm, PR = 7.5 cm, QS = 7 cm

Answer 1

In the cyclic quadrilateral PQRS, PQ = 4 cm, QR = 6 cm, PR = 7.5 cm and QS = 7 cm

Construction:

(i) Draw a line segment PQ = 4 cm

(ii) With P as the centre and radius 7.5 cm, draw an arc.

(iii) With Q as the centre and radius 6 cm, draw another arc meeting the previous arc as in the figure at R.

(iv) Join PR and QR.

(v) Draw the perpendicular bisectors of PQ and QR intersecting each other at O.

(vi) With O as the centre OP(=OQ=OR) as radius, draw the circumcircle of ∆PQR.

(vii) With Q as the centre and 7 cm radius, draw an arc intersecting the circle at S.

(viii) Join PS and RS.

(ix) Now, PQRS is the required cyclic quadrilateral.