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9 votes
1 answer
1k views

A chain of six circles associated with a conic

I found this problems three years ago. But I never have been a proof. Recently I posted in math.stackexchange.com. I am looking for a solution of the following problems: A chain of six circles ...
Oai Thanh Đào's user avatar
9 votes
0 answers
910 views

A new theorem (discovered in 2013) equivalent to Brianchon theorem (the old theorem) discovered in XIX century?

In 2013, I found a new problem as follows: Let six points $A_1$, $A_2$, ...$A_6$ lie on a circle $(O_1)$, and the six points $B_1$, $B_2$,...,$B_6$ lie on another circle $(O_2)$. If the quadruples $...
Đào Thanh Oai's user avatar
7 votes
1 answer
677 views

A problem of four conics

I found a remarkable theorem of four conics as follows some years ago. But it has no proof; I am looking for a proof: Theorem: Take three conics. Suppose that each of them touch a fourth conic at two ...
Đào Thanh Oai's user avatar
5 votes
1 answer
433 views

Golden ratio as a property of conic section (is it known?)

I am looking for a proof of a discovery as follows: Let $ABC$ be arbitrary triangle and $(\Omega)$ be an arbitrary circumconic of $ABC$ let $A'B'C'$ is its tangential triangle of $ABC$ respect to $(\...
Đào Thanh Oai's user avatar
1 vote
1 answer
352 views

Thirteen-point conic and four-point line, are they new?

We know that Five points determine a conic and Two Points Determine a Line. Here I found a simple construct of a conic through $7$ points (in PS I note that how the conic through thirteen points) and ...
Đào Thanh Oai's user avatar