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lvl10720-Turquoise
20-Turquoise
Dec 1, 2020 12:59 PM UTC
Question

Inscribed circle and altitude of triangle ?

Hello Everyone.
Given :
inscribed circle of triangle ABC touches its 3 sides at A', B', C'. (see Figure)
A'A'' is a altitude of triangle A'B'C'.
Prove :
C'B / C'A'' = B'C / B'A'' ( blue / green = red / pink )
I.PNG

 Thanks in advance for your time and help.
Regards.
Loi.

15 replies

ttokoro
ttokoro21-Topaz I
21-Topaz I
Dec 10, 2020 12:19 PM UTC

image.pngimage.pngimage.png

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t.t.
Werner_E
Werner_E25-Diamond I
25-Diamond I
Dec 10, 2020 2:51 PM UTC
@ttokoro wrote:

Not equal.

No, you are wrong! The two ratios ARE equal. For the example posted approx. 2.24224.

Check your calculations or your interpretation of the position of A". Guess you misinterpreted the latter. A'A'' is perpendicular to B'C' ! The coordinates are approx. A'' (3.92964 / 2.26219).

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    ttokoro
    ttokoro21-Topaz I
    21-Topaz I
    Dec 10, 2020 10:39 PM UTC

    Thanks. 

    image.png

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    t.t.
    -MFra-21-Topaz II
    21-Topaz II
    Dec 16, 2020 11:47 AM UTC

    Hi,

    the following video is my almost perfect animation about the triangle....:

    (view in My Videos)

    where: C'B=C1B, C'A''=C1A2, B'C=B1C and B'A''=B1A2

    triangolo.jpg

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