Why Does Ptolemy Start With :-P

Geometry Level 2

ABCDABCD is a cyclic quadrilateral with AB=11\displaystyle \overline{AB}=11 and CD=19\displaystyle \overline{CD}=19. PP and QQ are points on AB\overline{AB} and CD \overline{CD}, respectively, such that AP=6\displaystyle \overline{AP}=6, DQ=7\displaystyle \overline{DQ}=7, and PQ=27.\displaystyle \overline{PQ}=27. Determine the length of the line segment formed when PQ\displaystyle \overline{PQ} is extended from both sides until it reaches the circle.

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