In the image below there are two tangent semicircles. The side length of the square is 36cm.

What is the length of the radius of the yellow circle?

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Let the radius of yellow semicircle be r,

join the two centers of yellow and blue semicircles and this line intersets them at the point of tangency

hence we get a right triangle with hypotnuese = 18 + r

base =18

perpendicular = 36-r

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applying pythagoras theorem we get (18+r)^2 = 18^2 + (36-r)^2
we get r= 12 cms
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yes but if we raplace " r " by 12 in the equation we get that 900 = 900 not 12.

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