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Topic: Parallelogram Orthocenters
Replies: 7   Last Post: Oct 22, 2013 7:28 AM

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Avni Pllana

Posts: 503
Registered: 12/6/04
Re: Parallelogram Orthocenters
Posted: Oct 16, 2013 12:24 PM
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> Hi Avni,
>
> I suppose locating orthocenter by finding altitudes (
> = 2 Area of triangles / base ) etc. can be done.
>
> By geometric construction H1H2 ~ 7.57188, its
> component parallel to AB is 7. It can be noted that
> O, midpoint of DB or H1H2 is the anti-symmetric
> centre of opposite vertices of parallelogram ABCD.
>
> Regards
> Narasimham


Hi Narasimham,

you are right, but of course an analytical solution is required. I gave some numerical values of side lengths and angles only for clarity, but they are fully unimportant. Let it be AB=DC=a, AD=BC=b, and angle(BAD)= fi. There are some further interesting properties of this structure that I want to reveal after an analytical solution is provided.

Best regards,
Avni



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