Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.
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Sunday, January 25, 2015
Geometry Problem 1077: Chain of Equal Tangent Circles, Circular Sector, Area, Sangaku, Sacred Geometry
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S₁=1/2×(n-2)πr² = (n/2 - 1)πr²
ReplyDeleteS₂=1/2×2πr² + n×1/2 πr² = (n/2 + 1)πr²
S₂ - S₁ = 2πr²
http://s30.postimg.org/bdf0x1ccx/pro_1077.png
ReplyDelete1. From circle A, draw Ax//AM ( see sketch)
Let area of sector form by AB and Ax is a
Blue area of circle A – Yellow area of circle A= 2.a
2. From circle B draw Bx //Ax
Area of sector form by AB extension and BC is b
Blue area of circles A and B – Yellow areas of circles A and B= 2.(a+b)
Continue with circles C, D, E, F…. M
If all circles form a chain then areas of sectors a+b+…. m will be full circle radius r
Blue areas of all circles – yellow areas of all circles will be 2 times area of full circle= 2.pi.r^2