tmua 2022 Q19

tmua · Uk · paper1 1 marks Geometric Probability
Circle $C _ { 1 }$ is defined as $x ^ { 2 } + y ^ { 2 } = 25$
A second circle $C _ { 2 }$ has radius 4 and centre $( a , b )$ where
$$- 2 \leq a \leq 2 \text { and } - 3 \leq b \leq 3$$
If the centre of $C _ { 2 }$ is equally likely to be located anywhere within the given range, what is the probability that $C _ { 2 }$ intersects $C _ { 1 }$ ?
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Circle $C _ { 1 }$ is defined as $x ^ { 2 } + y ^ { 2 } = 25$

A second circle $C _ { 2 }$ has radius 4 and centre $( a , b )$ where

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

If the centre of $C _ { 2 }$ is equally likely to be located anywhere within the given range, what is the probability that $C _ { 2 }$ intersects $C _ { 1 }$ ?