Olympiad workbookIOQMStraight Lines

In a rectangle A B C D, E is the midpoint of A B: F is point on A C such that B F is perpendicular to A C and F E perpendicular to B D . Suppose B C=8 3 . Find A B .

Correct answer

Step-by-step solution

= 8 3 2 x = 4 3 x aligned & F A=2 x & F B=2 x & M B=F B x 2 =2 x 2 & M E^2+M B^2=B E^2=x^2 & x^2 ^2 +4 x^2 ^2 ^2 2 =x^2 & ^2 +4 ^2 ^2 2 =1 & 4 ^2 ^2 2 = ^2 & 16 ^4 =1 & ^2 = 1 4 = 1 2 & 4 3 x = 1 3 x=12 2 x=A B=24 Ans. aligned

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