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

+1 vote
1,444 views

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

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
``````
yes but if we raplace " r " by 12 in the equation we get that 900 = 900 not 12.
+1 vote

12cm

-Anonymous person

answer Jul 12, 2015 by anonymous
+1 vote

The yellow radius is 12 cm.

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

The answer is 12 cm. 36/3 because the yellow radius fit exatly 3 times proyected on the blue diameter.

divide the square in a 3 by 3 matrix this give 36 cms. squared divided by 9 =144 the square root of this is 12

–1 vote

how is possible

Similar Puzzles

In a square with a side length of 1, two quarter circles are drawn and a circle is inscribed between the quarter circles, as shown in the diagram.
What is the radius of the inscribed circle?

A square has side length equal to 1 meter. A circle is constructed through one corner of the square and tangent to the opposite two sides of the square. What is the area shaded in blue below, which is the area contained by the square and circle excluding the region where the two shapes overlap?