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Question:

If a circle C, whose radius is 3, touches externally the circle x² + y² + 2x - 4y - 4 = 0 at the point (2, 2), then the length of the intercept cut by this circle C on the x-axis is equal to?

3√2

√5

2√3

2√5

Solution:

x² + y² + 2x - 4y - 4 = 0
Centre = (-1, 2)
radius = √(1² + 2² + 4) = √9 = 3
(h, k) = (2, 2)
h = -1, and k = 2
C: (x - 5)² + (y - 2)² = 3²
p = |2|√1 = 2
AM = √3² - 2² = √5
AB = 2
AB = 2√5.