Timeline for Necessary and sufficient condition for quadrilateral to be cyclic
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 28 at 21:20 | comment | added | Fedor Petrov | @terceira should "are not" read as "are"? | |
| Jul 28 at 13:46 | comment | added | terceira | This is a brief comment to answer the question posed by @FedorPetrov above in the negative. There are non cyclic quadrilaterals for which the two quadrilaterals are not similar. The proof is purely computational and doesn't seem to provide any useful insights. | |
| Apr 26, 2021 at 17:16 | comment | added | Liam Baker | The 'if' direction is not hard to prove if 'nine-point centre' is replaced with 'centroid', since in that case $PQRS$ is always similar to $ABCD$. | |
| Apr 26, 2021 at 6:34 | comment | added | Francesco Polizzi | You are right: I will edit the answer adding your observation. – | |
| Apr 26, 2021 at 6:13 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| Apr 26, 2021 at 6:03 | comment | added | Fedor Petrov | Then it is not a stronger result: it does not prove the "if" part. | |
| Apr 26, 2021 at 5:33 | comment | added | Francesco Polizzi | @FedorPetrov: I do not know. It seems to me that Morley's proof only works for cyclic quadrilaterals, unless I am missing something. | |
| Apr 26, 2021 at 5:28 | comment | added | Fedor Petrov | It is similar when $ABCD$ is cyclic, but is it always similar? | |
| Apr 26, 2021 at 5:17 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| Apr 26, 2021 at 5:11 | history | answered | Francesco Polizzi | CC BY-SA 4.0 |