In-a-rectangle-ABCD-E-is-the-midpoint-of-AB-F-is-a-point-on-AC-such-that-BF-is-perpendicular-to-AC-and-FE-perpendicular-to-BD-Suppose-BC-8-3-Find-AB-

Question Number 20599 by Tinkutara last updated on 28/Aug/17

In a rectangle A B C D, E is the midpoint

of A B; F is a point on A C such that B F

is perpendicular to A C; and F E

perpendicular to B D . Suppose B C = 8 \sqrt{3} .

Find A B .

Answered by ajfour last updated on 29/Aug/17

Commented by Tinkutara last updated on 29/Aug/17

Thank you very much Sir!

Commented by ajfour last updated on 29/Aug/17

E F = A E = B E (r a d i i o f c i r c l e

w i t h E a s c e n t r e)

s o ∠ A F E = θ

∠ D B F = 90 ° - 2 θ, s o ∠ E B F = 2 θ

n o w ∠ A F E + ∠ E F B = 90 °

s o θ + 2 θ = 90 °

\Rightarrow \tan θ = \frac{B C}{A B} = \frac{8 \sqrt{3}}{A B} = \frac{1}{\sqrt{3}}

o r A B = 24 .

Facebook Tweet Pin