This image was shared with me on WhatsApp, found it interesting so sharing here.
In the picture you will see three circles inside a rectangle. The diameter of all the 3 circles are given, based on which you are supposed to find the length of AB.
Find the length of AB in the given picture.
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Answer: 7.348
Explanation:
As you can see in the picture, there are 3 circles inside the rectangle.
Let us call the 3 circles C1, C2 & C3.
Circle C1 touches the two adjacent sides of the rectangle and circle C2.
Circle C2 touches one side of the rectangle and the circles C1 & C2.
Circle C3 touches three sides of the rectangle and circle C2.
From the diagram, we know the diameters of the circles which are;
Diameter of circle C1 = 3cm,
Diameter of circle C2 = 4cm &
Diameter of circle C3 = 6cm
To solve this let’s break the rectangle into 2 pieces as shown in the figure below;
Applying Pythagoras theorem in the triangle AEC we get;
Now let’s look at the second part of the rectangle;
Applying Pythagoras theorem in the triangle BCF we get;
Now let’s put the rectangle together and find the length of A & B;
Good riddles