Q.19. Circle $C_1$ is defined as $x^2 + y^2 = 25$

A second circle $C_2$ has radius 4 and center $(a, b)$ where:

$$-2 \leq a \leq 2 \quad \text{and} \quad -3 \leq b \leq 3$$

If the center of $C_2$ is equally likely to be located anywhere within the given range, what is the probability that $C_2$ intersects $C_1$?

Answer Choices

• $\frac{1}{25}$
• $\frac{9}{25}$
• $\frac{16}{25}$
• $\frac{6 - \pi}{6}$
• $\frac{16 - \pi}{24}$
• $\frac{24 - \pi}{24}$

Solution

The correct answer is option 6: $\frac{24 - \pi}{24}$.