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funny trapezoid

Source: 2017 AMC 12B #24

February 16, 2017

geometryAMCAMC 12AMC 12 Btrapezoid2017 AMC 12B

Problem Statement

Quadrilateral

ABCD

has right angles at

B

and

C

,

\triangle ABC \sim \triangle BCD

, and

AB > BC

. There is a point

E

in the interior of

ABCD

such that

\triangle ABC \sim \triangle CEB

and the area of

\triangle AED

is

17

times the area of

\triangle CEB

. What is

\tfrac{AB}{BC}

?

<span class='latex-bold'>(A) \ </span> 1+\sqrt{2} \qquad <span class='latex-bold'>(B) \ </span> 2+\sqrt{2}\qquad <span class='latex-bold'>(C) \ </span> \sqrt{17}\qquad <span class='latex-bold'>(D) \ </span> 2+\sqrt{5} \qquad <span class='latex-bold'>(E) \ </span> 1+2\sqrt{3}

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