## Re: [EMHL] Altitudes as diameters of circles [variation]

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• On Thursday, February 7, 2002, at 02:00 PM, Antreas P. Hatzipolakis ... BHb, CHc ... Similarly define the circles (Kbc),(Kba);(Kca),(Kcb) H a = the 2nd
Message 1 of 20 , Feb 7, 2002
On Thursday, February 7, 2002, at 02:00 PM, Antreas P. Hatzipolakis
wrote:

> Another variation:
>
> AHa, AHb, AHc = altitudes.
BHb, CHc
>
> Hab = Orth. Proj. of Ha on AB,
> Hac = Orth. Proj. of Ha on AC.
>
>
> (Kab) = the circle with diameter HaHab
> (Kac) = the circle with diameter HaHac

Similarly define the circles (Kbc),(Kba);(Kca),(Kcb)

H'a = the 2nd intersection of (Kab),(Kac)
[the first is Ha]
that is, HaH'a is the common chord of (Kab),(Kac)

H'b = the 2nd intersection of (Kbc),(Kba)
[the first is Hb]

H'c = the 2nd intersection of (Kca),(Kcb)
[the first is Hc]

Are the triangles

1. HaHbHc, H'aH'bH'c

2. ABC, H'aH'bH'c

perspective?

Antreas

>
> A'= (2nd tangent to (Kab) from B) /\ (2nd tangent to (Kac) from C)
> [the 1st tangent is AB] [the 1st tangent is AC]
>
> Similarly B', C'.
>
> A
> /\
> / \
> / \
> / \
> / \
> / \
> / \
> Hab \
> / Hac
> / Kab \
> / Kac \
> B-----------Ha----------C
>
> A'
>
>
>
> The triangles ABC, A'B'C' are perspective.
>
> 1
> Perspector: ( ----------------- ::) = (tanAsin^2A ::) in Barycentrics.
> cotA*(1 + cot^2A)
>
>
> Antreas
>
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