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wait if this is english why do i have to translate it???

Source: 2022 AIME I #3

February 9, 2022

AMCAIMEAIME I

Problem Statement

In isosceles trapezoid

ABCD

, parallel bases

\overline{AB}

and

\overline{CD}

have lengths

500

and

650

, respectively, and

AD=BC=333

. The angle bisectors of

\angle{A}

and

\angle{D}

meet at

P

, and the angle bisectors of

\angle{B}

and

\angle{C}

meet at

Q

. Find

PQ