Q5 of 19 Page 176

Let us draw the rectangle PQRS having PQ = 4 cm, and QR = 6 cm. Let us draw the diagonals of the rectangle. Let us write by calculating the position of the centre of the circum-circle of ΔPQR and the length of circum radius without drawing. By drawing circumcircle of ΔPQR, let us verify.

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



More from this chapter

All 19 →
3

Given, AB = 5cm, ∠BAC = 30°, ∠ABC = 60°,

AB = 5cm, ∠BAD = 45°, ∠ABD = 45°;


Let us draw ΔABC and ΔABD in such a way that the point C and D lie on opposite sides of AB. Let us draw the circle circumscribing ΔABC. Let us write the position of the point D with respect to circumcircle. Let us write by understanding what other characteristics we are observing here.

 4

We draw a quadrilateral ABCD having AB = 4 cm, BC = 7 cm CD = 4 cm, ∠ABC = 60°, ∠BCD = 60°. Let us draw the circle circumscribing ΔABC and write what other characteristics we observe.

 6

If any circular picture is given, then how shall we find its centre? Let us find the centre of the circle in the adjoining figure.

 1

Let us draw the following triangles and by drawing incircle of each circle, let us write by measuring the length of inradius in each case.

the lengths of three sides are 7 cm., 6 cm., and 5.5 cm.