Multiple choice

The common chord of the circles $x^{2} + y^{2} - 4x - 4y = 0$ and $2x^{2} + 2y^{2} = 32$ subtends at the origin an angle equal to

  1. $\dfrac {\pi}{3}$
  2. $\dfrac {\pi}{4}$
  3. $\dfrac {\pi}{6}$
  4. $\dfrac {\pi}{2}$
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D Correct answer
Explanation

Circle 1: x^2 + y^2 - 4x - 4y = 0. Circle 2: x^2 + y^2 = 16. Subtracting gives the common chord: -4x - 4y = -16, or x + y = 4. The chord is at distance 2*sqrt(2) from the origin. The angle subtended at the origin is 90 degrees.

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