Explanation

We know that circumference of a circle = \(\pi \times d\). Here D is diameter of circle.

One smaller circle has diameter PR and other is QR.

Diameter of the largest circle is PQ. Now PQR lie on the same line.

PR + QR = PQ

multiplying \(\pi\) both side

\(\pi \times PR + \pi \times QR = \pi \times PQ\).

Circumference of smaller circle with diameter PR + Circumference of smaller circle with diameter QR = Circumference of larger circle with diameter PQ.


"it is said in the question that R lies on a segment", I dont think it is safe to assume that the line segment shown and described in the circle is a diameter. in which case answer should be D...Please correct me if I am wrong.


Quantity B = Quantity A.

Hence C is correct option.

Even though your explanation is still not clear, I will trust your reasoning on this one. Anytime I see a similar question, even if it has 5 circles inside the major circle and they are tangent, I will assume the circumference is equal to that of the major circle.