# There are two tangent semicircles as per Image. The side length of square is 36cm. What is the radius of yellow circle?

+1 vote
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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?

posted Jun 13, 2015

## 4 Solutions

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

``````     applying pythagoras theorem we get (18+r)^2 = 18^2 + (36-r)^2

we get r= 12 cms
``````
solution Jun 25, 2015
+1 vote

12cm

-Anonymous person

solution Jul 12, 2015 by anonymous

solution Sep 22, 2016

how is possible

Confirmed by simply measuring it with a ruler:

The yellow 1/2 circle extends 2/3 along the side of the square,
Thus 2/3*36 = 24 cm diameter
Therefore 1/2* 24 = 12 cm.radius

solution Oct 26, 2016

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