Charles Link's latest activity

Okay. ## c^2=a^2+(2R)^2-2\cdot a\cdot2R\cdot\cos(\angle ADC) ## ## c^2=x^2+b^2-2\cdot x\cdot b\cdot\cos(\angle ABC) ## I want to offer...

additional numbers to complete the set with 5 in the denominator for ## m ##: ## m=9/5 ##, ## a=59 ##, ## b=227 ##, ## x=151 ## ##...

Going back to post 56, I now tried, just for the fun of it, to see if I could get another solution using @daverusin 's method of post...

Although I slighted @Gavran by not mentioning his attempt, I don't think anyone had called out Ptolemy's Theorem by name. How often do...

In post 43 @Gavran cited it on his very last line in parentheses. It is so easy to overlook something like that though, because this...

@hutchphd It gets harder as we get older. I am 70 now. We sort of have an excuse. Too many of the younger ones though I see are...

Yes indeed. Through laziness I did not really look at the attempt.......bad form on my part (apologies!)

Looking back over things, I do think @daverusin in post 41 has something of considerable merit. With his method, which I figured out...

@Gavran I presume in your solution that you plugged in ## R=x ##. You then get ## a^2-b^2+3x^2 =2a^2+ab ## so that ## 3x^2=a^2+b^2+ab...

You are right. There is one more approach which is based on the figure from the post #39 and it is simpler than the one I have provided...

Looking back to the other posts, I see @Gavran also used Ptolemy's theorem previously in post 43, but the post 52 method gets the...

@hutchphd Here is the solution: ## (ac)(bd)=2x^2+(11)(2) ## from Ptolemy ## (ac)^2=4x^2-2^2 ## from Pythagoras and Thales ##...

Please feel free. I have had an exhausting week and seem disinclined to do anything (feeling each of my 73 yrs I guess.....ah, well. I...

@hutchphd a super result. :) With a couple algebraic steps one gets ## 3x^2=11^2+2^2+(2)(11) ##. I'll let you write it out, but if you...

There is also a lovely theorem by Ptolemy that deals with cyclic quadrilaterals. I think that will work......not an intuitive result...