question_answer

If (\[\alpha ,\]\[\beta \]) is a point on the circle whose center is on the x-axis and which touches the line \[x+y=0\]at (2,-2) then the greatest value of \[\alpha \]is

A) \[4-\sqrt{2}\]  

B) 6

C) \[4+2\sqrt{2}\]          

D) \[4+\sqrt{2}\]

Correct Answer: C

Solution :

[c] if (a, 0) is the center C and P is (2, -2), then \[\angle COP=45{}^\circ \]. Since the equation of OP is \[x+y=0\], we have \[OP=2\sqrt{2}=CP\] Hence, OC=4, The point on the circle with the greatest x coordinate is B. \[\alpha =OB=OC+CB=4+2\sqrt{2}\]