Answer :

In the rectangle PQRS, we join PR and QS. We see that PQR is a right-angled triangle. For a right angle triangle, the circumcenter is the midpoint of the hypotenuse and circumradius is half of the length of the hypotenuse. The hypotenuse PR = √(PQ)2 + (QR)2 = √(4)2 + (6)2 = 7.21cm.


Thus, circumradius = 7.21/2 = 3.6cm


Steps of Construction:


1. Construct rectangle PQRS of given dimensions.



2. Draw perpendicular bisector of PQ.



3. Draw perpendicular bisector of QR.



4. The point of intersection is the circumcenter. Name it as O.


5. With O as center and OR as radius, draw a circle.


6. The circle passes through P,Q and R and is thus the circumcircle of this triangle.


7. We measure the circumradius, OR = 3.6cm



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