Question

2. PQ = 7.5 Ħoto ZQPR = 45°, ZPQR = 75°; PQ = 7.5 ĦHO ZQPS = 60°, ZPQS = 60°; #OHO​

Answer 1

Answer:

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