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

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Peter Scales

Posts: 192
From: Australia
Registered: 4/3/05
Re: Parallelogram Orthocenters
Posted: Oct 16, 2013 12:06 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> Let ABCD be a parallelogram such that AB=DC=10, and
> AD=BC=6,
> and angle(BAD)=60°. Let H1,H2 be the orthocenters of
> triangles ABD and CDB respectively. Determine the
> distance between H1 and H2.
> Best regards,
> Avni

A pretty figure.
Two normals divide the parallelogram sides into 3+7 and 1+5 so that the orthocenters are the opposite corners of a rectangle 7x(3.sqrt3-2.2/sqrt3) = 7 x (5/sqrt3)
whence H1H2 = sqrt(172/3) = 2.sqrt(43/3)

Regards, Peter Scales.

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