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#24 Geo has come back!

Source: 2021 AMC 12B (Fall) #24

November 17, 2021

AMCAMC 12AMC 12 B

Problem Statement

Triangle

ABC

has side lengths

AB = 11, BC=24

, and

CA = 20

. The bisector of

\angle{BAC}

intersects

\overline{BC}

in point

D

, and intersects the circumcircle of

\triangle{ABC}

in point

E \ne A

. The circumcircle of

\triangle{BED}

intersects the line

AB

in points

B

and

F \ne B

. What is

CF

?

<span class='latex-bold'>(A) </span> 28 \qquad <span class='latex-bold'>(B) </span> 20\sqrt{2} \qquad <span class='latex-bold'>(C) </span> 30 \qquad <span class='latex-bold'>(D) </span> 32 \qquad <span class='latex-bold'>(E) </span> 20\sqrt{3}

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