One of most recent mathematics problem is this one. In the problem there are three circle inside of a rectangle. The problem is about the radius of the circle. Let’s see the problem description.

## Problem

There are three circle in a rectangle such that one circle touch 3 sides of the rectangle, another touch 2 sides of the rectangle, and the rest one touch 1 side of the rectangle and other 2 circles. What is the distance between two point on same side of the rectangle where first and second circle touches? In the below picture the length of AB.

## Solution

To understand the problem correctly see the picture carefully.

Here the diameter of the largest circle is 6cm. Other two circle have diameter of 3cm and 4cm respectively.

First of all find the radius of each circle dividing the diameter by 2. See the picture below.

Now draw a parallel line to AB at central point of middle circle. Then connect the center of neighbor circles. Connect the center of red circle with the center of blue circle and connect the center of blue circle and green circle. Draw to perpendicular from center of red circle and green circle to the parallel line of AB drawn.

Now, calculate the length of perpendicular and combined radius.

Combined radius for green and blue circle is = 1.5cm + 2cm = 3.5cm.

Combined radius for blue and red circle is = 2cm + 3cm = 5 cm.

Length of perpendicular from green circle is = diameter of red circle – radius of blue circle – radius of green circle.

So, length of perpendicular from green circle is = 6cm – 2cm – 1.5cm = 2.5cm

Length of perpendicular from red circle is = diameter of red circle – redius of red circle – radius of green circle.

So, length of perpendicular from red circle is = 6cm – 3cm – 2cm = 1cm

Now, find the land from the perpendicular and hypotenuse using Pithagoras’s Identity.

Hope you got √6 and 2√6.

Sum both land. That is the result.

I expect you got 3√6. If you got something else please read the solution again.

If you have any confusion you can comment.

Comment how you feeling after reading this.

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