IBPS PO Quantitative Aptitude: Circles questions with solutions

Q1. The distance between the centres of two adjacent circles is 15 cm. If the shortest distance between the edges of the circles is 4.5 cm and the difference between their radii is 3.5 cm, then find the area of the bigger circle.

1. 22 cm²
2. 77 cm²
3. 308 cm²
4. 154 cm²

Answer: 154 cm²

For two separate circles, centre distance = sum of radii + shortest gap. So, $r_1 + r_2 = 15 - 4.5 = 10.5$. Given $r_1 - r_2 = 3.5$, the bigger radius is 7 cm. Area of the bigger circle is $\pi r^2 = \frac{22}{7} \times 49 = 154\text{ cm}^2$.