Peas in a Pod
Five peas are all tangent to two nonparallel lines and tangent to its neighbor. The largest pea has a radius of
and the smallest pea has a radius of
.
What is the middle pea's radius?
The answer is 12.
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Geometric series. I'll use x to denote common ratio. We have R2=8x R3=8x^2 R4=8x^3 R5=18=8x^4
From last equation we get: x^4=18/8=9/4 So x^2 = 3/2
So the middle one r3 = 8*3/2 = 12