A geometry. . Trigonometry question.
Rhombus with many circles in it..
Find the radii of the orange circle and the dashed circle.
AB = a. Angle A = 60 deg.
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R= radius of blue circle.
r = radius of yellow/orange circle.
Ignore the green circle.
a = side AB BC CD DA = 1.
O = center of Rhombus.
OA = a*(sqrt3)/2.
OB = a/2.
E= center of leftmost orange circle
F = center of topmost orange circle.
BF = 2r/sqrt3.... AE = 2r.
OF^2= (R+r)^2-(R-x)^2
OF= a/2 - BF.
.
R+r = sqrt3 *a/4
Sqrt(4Rr) + 2r/sqrt3 = a/2.
.
R = 3r.
r = sqrt3* a/16...
R = 3 sqrt3* a/16.
r = radius of yellow/orange circle.
Ignore the green circle.
a = side AB BC CD DA = 1.
O = center of Rhombus.
OA = a*(sqrt3)/2.
OB = a/2.
E= center of leftmost orange circle
F = center of topmost orange circle.
BF = 2r/sqrt3.... AE = 2r.
OF^2= (R+r)^2-(R-x)^2
OF= a/2 - BF.
.
R+r = sqrt3 *a/4
Sqrt(4Rr) + 2r/sqrt3 = a/2.
.
R = 3r.
r = sqrt3* a/16...
R = 3 sqrt3* a/16.
kvnmurty:
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