3d trig help (1 Viewer)

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HSC
2015
Hey guys u know mx1 2005 hsc question 7a g0(soz picture too big to upload), the answer says to find PT (which turns out to be 2050m) and use triangle PTA (say 'A' is the top corner of circle) and it says here that it is a right angle triangle, how can we assume? And also how can we assume pt bisects p into alpha/2?
 

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