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For a circle with center point P, chord XY is the perpendicular bisector of radius AP (A is a point on the edge of the circle). What is the length of chord XY?

(1) The circumference of circle P is twice the area of circle P.

(2) The length of Arc XAY = 2π3 .

If we let Z represent the intersection point between AP and XY, and ZP=r, XP=2r, XZ=sqrt(3)r, there is one variable (r), and 2 equations are given from the 2 conditions; there is high chance (D) will be our answer.

From condition 1, 2(phi)r=2(phi)r^2, r=1. This condition is sufficient,

From condition 2, angle AXP=120 deg, and the length of Arc XAY=2(phi)r(120/360)=2(phi)/3. r=1. This conditions is sufficient as well.

1)=2), so the answer becomes (D).

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