Q2 of 19 Page 176

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.

Steps of Construction:



1. Construct ΔPQR of given dimensions.


2. Construct ΔPQS of given dimensions such that R and S lie on the same side of PQ.



3. Draw perpendicular bisector of PQ.



4. Draw perpendicular bisector of QR.



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 P,Q and R and is thus the circumcircle of this triangle.


We observe that the circumcircle also passes through S, i.e. S lies on the circle. This is because sum of the adjacent angles of the base of both the triangles are equal. That makes ∠PRQ = ∠PSQ.


We know that angle in the same segment of a circle are equal. That’s why S 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.

A triangle of which length of one side is 6.7 cm and the two angles adjacent to this side are 75o and 55o.

 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.

 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.