Maths Paper 1, November 2024, question 3.3

A circle of radius 20 cm is drawn. A second circle is drawn so that it passes through the centre of the first circle and touches the first circle from the inside. A third circle is drawn in the same way inside the second circle: it passes through the centre of the second circle and touches the second circle from the inside. The process carries on forever, as shown in the diagram below. Which circle in this pattern has a diameter of $\frac{5}{64}$ cm?