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• Let ABC be a triangle with A = 90 d. Let D be a point in AC such that inradius of BDA = inradius of BDC := d Find all triangles ABC with a,b,c,d integers.
Message 1 of 3 , Jun 23, 2011
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Let ABC be a triangle with A = 90 d.

Let D be a point in AC such that inradius of BDA = inradius of BDC := d

Find all triangles ABC with a,b,c,d integers.

Antreas

PS. We can use the formula c^2 = 2d^2 / (2d - r) (application of
this<http://anthrakitis.blogspot.com/2010/12/concurrent-externaltangents-of-three.html>
)

Antreas

[Non-text portions of this message have been removed]
• Correction: Let ABC be a triangle with A = 90 d. Let D be a point in AC such that inradius of BDA = inradius of BDC := d Find all triangles ABC with a,b,c,d
Message 1 of 3 , Jun 23, 2011
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Correction:

Let ABC be a triangle with A = 90 d.

Let D be a point in AC such that inradius of BDA = inradius of BDC := d

Find all triangles ABC with a,b,c,d integers, gcd(a,b,c) = 1 (primitive
heronian right triangles).

Antreas

PS. We can use the formula c = 2d^2 / (2d - r) (application of
this<http://anthrakitis.blogspot.com/2010/12/concurrent-externaltangents-of-three.html>
)

[Non-text portions of this message have been removed]
• Solution HERE (hope there are no computational errors!) APH On Thu, Jun 23, 2011 at 2:02 PM, Antreas
Message 1 of 3 , Jun 24, 2011
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(hope there are no computational errors!)

APH

On Thu, Jun 23, 2011 at 2:02 PM, Antreas Hatzipolakis
<anopolis72@...>wrote:

>
> Let ABC be a triangle with A = 90 d.
>
> Let D be a point in AC such that inradius of BDA = inradius of BDC := d
>
> Find all triangles ABC with a,b,c,d integers.
>
>
> Antreas
>
> PS. We can use the formula c^2 = 2d^2 / (2d - r) (application of this<http://anthrakitis.blogspot.com/2010/12/concurrent-externaltangents-of-three.html>
> )
>
> Antreas
>

--
http://anopolis72000.blogspot.com/

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