Question

The common chord of x² + y² – 4x – 4y = 0 and x² + y² = 16 subtends at the origin an angle equal to

• A. $\frac{\pi}{6}$
• B. $\frac{\pi}{4}$
• C. $\frac{\pi}{3}$
• D. $\frac{\pi}{2}$

Answer 1

Answer: (D)

$\frac{\pi}{2}$

Answer 2

The equation of the common chord of the circles

x² + y² – 4x – 4y = 0 and x² + y² = 16 is x + y = 4

which meets the circle x² + y² = 16 at points A(4, 0) and

B(0, 4). Obviously OA⊥OB, where O is the origin.

Hence the common chord AB makes a right angle at the centre of the circle x² + y² = 16