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The common chord of \mathrm{ x^2+y^2-4 x-4 y=0} and \mathrm{x^2+y^2=4^2} subtends an angle \mathrm{\alpha} at the origin, then \mathrm{\alpha} equals

Option: 1

30^{\circ}


Option: 2

45^{\circ}


Option: 3

60^{\circ}


Option: 4

90^{\circ}


Answers (1)

best_answer

Equation of common chord of circles \mathrm{x^2+y^2-4 x-4 y=0} and \mathrm{x^2+y^2=4^2\, \, is \, \, x+y=4}, which meet the circle \mathrm{x^2+y^2=4^2} at the points \mathrm{A(4,0)\, \, and \, \, B(0,4)}. Obviously \mathrm{O A \perp O B}. Hence, common chord AB makes a right angle at the centre of the circle whose radius is 4 .

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