Geometry Problem 1495. Post your solution in the comment box below.

Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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Trigonometry Solution

ReplyDeleteIf 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