Question

PQRS is a common diameter of three circles. The area of the middle circle is the average of the area of the other two. If PQ = 2 and RS = 1 then the length QR is

Answer 1

Given:

PQRS is a common diameter of three circles. The area of the middle circle is the average of the area of the other two.  

To find:

If PQ = 2 and RS = 1 then the length QR is

Solution:

The area of a circle in terms of diameter is given by,

A =  πd²/4

From given, we have, the area of the middle circle is the average of the area of the other two.  

[πPQ²/4 + πRS²/4]/2  = πQR²/4

[PQ² + RS²]/2 = QR²

[2² + 1²]/2 = QR²

[4 + 1]/2 = QR²

5/2 = QR²

∴ QR = √(5/2)

∴ The length of QR is √(5/2)