+0  
 
0
79
2
avatar+83 

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

 Jan 20, 2021
 #1
avatar+116126 
+2

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....

 

cool cool cool

 Jan 20, 2021
 #2
avatar
+1

Max is 20, when EF is parallel to AB.

I don't have time to type in solutions, (I have two), at the moment, but will try to do so later.

 

Tiggsy.

 Jan 21, 2021

50 Online Users

avatar
avatar