Question

Draw a line segment PQ = 8 cm. Draw its perpendicular bisector which will give the mid-point of PQ. Mark it as O. With O as centre and OP or OQ as radius, draw a circle . The circle cuts
the perpendicular bisector at points R and S. What is the line ROS with respect to the circle​

Answer 1

Steps of Construction :

1. With P and Q as centers, draw arcs on both sides of PQ with equal radii. The radius should be more than half the length of PQ.  

2. Let these arcs cut each other at points R and RS  

3. Join RS which cuts PQ at D. Then RS=PQ. Also ∠POR=90  

Hence, the line segment RS is the perpendicular bisector of PQ as it bisects PQ at P and is also perpendicular to PQ. On measuring the lengths of PR=4cm, QR=4 cm Since PR=QR, both are 4cm each  

hence

PR=QR.

Answer 2

Answer:

Steps of Construction :  

1. With P and Q as centers, draw arcs on both sides of PQ with equal radii. The radius should be more than half the length of PQ.  

2. Let these arcs cut each other at points R and RS  

3. Join RS which cuts PQ at D. Then RS=PQ. Also ∠POR=90  ∘ .

Hence, the line segment RS is the perpendicular bisector of PQ as it bisects PQ at P and is also perpendicular to PQ. On measuring the lengths of PR=4cm, QR=4 cm Since PR=QR, both are 4cm each  

∴PR=QR.