Circles C1 and C2 lie in the plane. C1 has center at A and radius 5, and C2 has center at B and radius 7. The distance from A to B is 10. The two circles intersect in points P and Q. Let L be a line through P that intersects C1 at P and E and intersects C2 at P and F. Let x be the longest possible length for EF. Then
(A) x ≤ 19 (B) 19 < x ≤ 20 (C) 20 < x ≤ 21 (D) 21 < x ≤ 22 (E) 22 < x
Strictly through a little experimentation, I get that the greatest length of EF is ≈ 19.98
However.....I'd like to see if someone knows the method of generating a definite solution and how they get the result....