Friday, September 2, 2022

Geometry Problem 1495: Circle, Parallel Chords, 30 Degree Angle, Radius Squared

Geometry Problem 1495. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

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Geometry Problem 1495: Circle, Parallel Chords, 30 Degree Angle, Radius Squared

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1 comment:

  1. Trigonometry Solution

    If O is the centre, Tr.s AOC, COE, DOF, BOD are all equilateral

    So if < AOB = 2@ then < EOF = 120-2@

    AB = 2r.sin@
    CD = 2r.sin(60+@) = r.(sqrt3.cos@ + sin@)
    EF = 2r.sin (60-@) = r.(sqrt3.cos@ - sin@)

    Squaring and adding

    AB^2 + CD^2 + EF^2
    = r^2.( 4sin^2 @ + sin^2 @+ 3cos^2 @ + 2sqrt3.cos@sin@
    + sin^2 @ + 3cos^2 @ - 2sqrt3.cos@sin@)
    = r^2.(6sin^2 @ + 6 cos^2 @)
    = 6r^2

    Sumith Peiris
    Moratuwa
    Sri Lanka

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