Friday, January 8, 2010

Fox 223

Still simple, aint it?

2 comments:

  1. It's more algebra than geometry

    Let the sides of the rhombus = s; use the theorem about chords crossing inside a circle:

    (1) a(s + v) = z(s + b)
    (2) b(s + z) = t(s + c)
    (3) c(s + t) = u(s + d)
    (4) d(s + u) = v(s + a)


    (1) – (4) as – vs = zs + zb – ds – du
    (2) – (1) bs – zs = ts + tc – as – av
    (3) – (2) cs – ts = us + ud – bs – bz
    (4) – (3) ds – us = vs + va – cs – ct


    rearrange:

    a = z + (zb/s) – d – (du/s) + v
    b = t + (tc/s) – a – (av/s) + z
    c = u + (ud/s) – b – (bz/s)+ t
    d = v + (va/s) – c – (ct/s) + u

    add the last 4 equations:

    a + b + c + d = t + u + v + z

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  2. Correct. I think the relationship can be seen with smaller number of steps. Expand the first 4 equations and add them up. It should stand out right away.
    Thank you Bob.

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