Q3 of 19 Page 176

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.

Steps of Construction:


1. Construct ΔABC of given dimensions.



2. Construct ΔABD of given dimensions such that C and D lie on the opposite side of AB.



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 OR 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 the circumcircle also passes through D, i.e. D lies on the circle. This is because the sum of ∠A and ∠B is 180°. We know that in a cyclic quadrilateral, sum of the opposite angles of a quadrilateral is 180°. That’s why D lies on the circle.


More from this chapter

All 19 →
1

Let us draw the following triangles. By drawing the circum-circle in each case, let us write the position of circum-centre and the length of circum-radius by measuring it.

ABC is triangle of which BC = 5 cm., ∠ABC = 100° and AB = 4 cm.

 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.

 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.

 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.