2022 SSMO Team Round Problems/Problem 5
Problem
Consider the following rectangle 
where 
If ![\[CD=CT_2, 4T_2P_2=2DP_1=AC, [ADP_1C]=33, \text{ and }[ABP_2C]=34,\]](http://latex.artofproblemsolving.com/8/4/3/8433536ddd4f434d544848301fbdf62184f1116d.png)
find the value of ![$[P_1CP_2A].$](http://latex.artofproblemsolving.com/e/7/b/e7b7f79c632fa97d99155de285804ee60d8a76d8.png)
(Note that ![$[ABC]$](http://latex.artofproblemsolving.com/d/3/3/d33cc80fa8f093e155c5be46d2e5d9da3d7e1ef5.png)
is the area of 
.)
![[asy] unitsize(0.25cm); dot((0,0)); dot((12,0)); dot((12,16)); dot((0,16)); draw((0,0)--(12,0)--(12,16)--(0,16)--(0,0)--cycle); dot((8,22)); dot((17,4)); dot((8,16)); dot((12,4)); label("$A$", (0,0), SW); label("$B$", (12,0), SE); label("$C$", (12,16), NE); label("$D$", (0,16), NW); label("$P_1$", (8,22), NE); label("$P_2$", (17,4), SE); label("$T_1$", (8,16), SE); label("$T_2$", (12,4), SW); draw((8,22)--(8,16),dashed+linewidth(.5)); draw((12,4)--(17,4),dashed+linewidth(.5)); [/asy]](http://latex.artofproblemsolving.com/a/e/5/ae56fa6d575f87aa09fa96f2ce1475e077e2019a.png)
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