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For the circles x² + y² - 4x - 4y = 0 and x² + y² = 16, what angle is subtended at the origin by their common chord?

1. π/6
2. π/4
3. π/3
4. π/2

Correct answer: π/2

Solution

Subtracting the circle equations gives the common chord x+y=4, which meets x^2+y^2=16 at (4,0) and (0,4). These two points subtend a right angle (pi/2) at the origin.

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