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hints/help for MCIV chp11 problems

 
 
TuAndrew的头像
hints/help for MCIV chp11 problems
TuAndrew - 2020年10月8日 Thursday 20:37
 
For problem 11.10, it asks to prove ptolemy's inequality. I have tried creating a point E like the proof of ptolemy's theorem started with, but I did not get too far with that. I have also tried using law of sines, but also got stuck.  Can I have some help/hints for this problem?


for Problem 11.11, I am a bit confused on what to do and stuck on how to start. Could I have some pointers on how to start, and the main idea/goal for this proof?

Thank you.

 
WangDr. Kevin的头像
Re: hints/help for MCIV chp11 problems
WangDr. Kevin - 2020年10月9日 Friday 01:14
 

11.10: Finding the point E is the right way to go.  Instead of proving equality, you use Triangle Inequality.

11.11: Proving Ptolemy's Theorem and Simson's Theorem are equivalent.  You need to formulate the problem first.  Say you are trying to prove Simson's Theorem.  Look at the conditions of Simson's Theorem.  Use those, and apply Ptolemy's Theorem in the process (we are assuming Ptolemy's Theorem is true, and prove Simson's Theorem).  Then you need to prove the other direction: assuming Simson's Theorem is right, prove Ptolemy's.

 
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