What a Circle

Geometry Level 2

A small circle inscribed between two indentic big circle. The three circles are also tangent to a line. If the radius of the big circle is 10 10 , find the radius of the small circle


The answer is 2.5.

Jason Chrysoprase by Jason Chrysoprase , 18, Indonesia

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1 solution

From the above figure, we can conclude with pythagorean theorem that

1 0 2 + ( 10 − r ) 2 = ( 10 + r ) 2 10^2 + ( 10 - r )^2 = ( 10 + r )^2

100 + r 2 − 20 r + 100 = r 2 + 20 r + 100 100 + r^2 - 20r + 100 = r^2 + 20r + 100

40 r = 100 40r= 100

r = 2.5 r = \color{#20A900}{\boxed{2.5}}

S I M P L E A N D E A S Y SIMPLE \space AND \space EASY

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