1
Question
Construct a cyclic quadrilateral PQRS with PQ=4cm, QR=6cm, PR=7.5cm, QS=7cm.
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Solution
In the cyclic quadrilateral PQRS, PQ=4cm, QR=6cm, PR=7.5cm and QS=7cm.
Construction:
(i) Draw a rough diagram and mark the measurements.
(ii) With P as centre and radius 7.5cm, draw an arc.
(iii) With Q as centre and radius 6cm, 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 ΔPQR.
(vii) With Q as centre and 7cm radius, draw an arc intersecting the circle at S.
(viii) Join PS and RS.
(ix) Now, PQRS is the required cyclic quadrilateral.
Construction:
(i) Draw a rough diagram and mark the measurements.
(ii) With P as centre and radius 7.5cm, draw an arc.
(iii) With Q as centre and radius 6cm, 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 ΔPQR.
(vii) With Q as centre and 7cm radius, draw an arc intersecting the circle at S.
(viii) Join PS and RS.
(ix) Now, PQRS is the required cyclic quadrilateral.
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