Q4 of 19 Page 176

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.

Steps of Construction:


1. Construct quadrilateral ABCD of given dimensions.



2. We join A to C.


3. Draw perpendicular bisector of AB.



4. Draw perpendicular bisector of BC.



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


6. With O as center and OC as radius, draw a circle.



7. The circle passes through A,B and C and is thus the circumcircle of this triangle.


We observe that ABCD is a cyclic quadrilateral as all the points A,B,C and D lie on the circle.


More from this chapter

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2

Given, PQ = 7.5cm, ∠QPR = 45°, ∠PQR = 75°;

PQ = 7.5cm, ∠QPS = 60°, ∠PQS = 60°;


Let us draw ΔPQR and ΔPQS in such a way that the points R and S lie on the same side of PQ, let us draw the circum circle of ΔPQR and let us observe and write the position of the point S within, on and out side the circum circle. Let us find out its explanation.

 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.

 5

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.

 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.