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Topic: Same intersection angles in ellipse
Replies: 6   Last Post: Oct 29, 2013 3:11 PM

 Messages: [ Previous | Next ]
 Avni Pllana Posts: 546 Registered: 12/6/04
Re: Same intersection angles in ellipse
Posted: Oct 27, 2013 11:29 AM

> I have used another property, viz., the product of
> normals. ( It may be the same, but seen some other
> way! )
> http://i42.tinypic.com/2afagbk.jpg
>
> F1 P+ F2 P = 2 a
> F1 P+ F1 Q = 2 a, given.
> So F1 Q = F2 P
> Likewise, F1 P = F2 Q
> F1, P, F2 and Q are vertices of a parallelogram and
> it is required to find inclination si of F1 P to
> tangent at P. Product of normals F1 P sin(si)* (2 a-
> F1 P) sin(si) = b^2 allows finding si for any F1 P.
>
> Best Regards,
> Narasimham

Hi Narasimham,

the product of normals d1*d2 = const, also holds for any two isogonal conjugate points P,Q with respect to an arbitrary triangle, where d1,d2 denote distances of P,Q from a triangle side.

Best regards,
Avni

Date Subject Author
10/19/13 Narasimham
10/20/13 Narasimham
10/20/13 Peter Scales
10/26/13 Narasimham
10/27/13 Avni Pllana
10/29/13 Peter Scales
10/29/13 Narasimham