Question

Three circles of diameter 3 cm, 4 cm and 6 cm are inscribed inside a rectangle, with the middle circle touching the other two circles, as shown. Find the distance AB.

Answer 1

Given:

• Radius of 1st circle = 1.5  cm
• Radius of 2nd circle = 2 cm
• Radius of 3rd circle = 3 cm

To Find:

   Distance AB

Step-by-step explanation:

We have to find the distance between A and B

Considering circle 2nd and circle 3rd

• leg = 3-2 = 1 cm

Hypotenuse

• = 2+3
• = 5 cm

Using the Pythagorean Theorem

We will find the other leg of perpendicular

• h² = p² + b²
• 5² = p² + 1²
• p² = 25-1
• p =√24
• p = 2√6 cm

Now, considering circle 1st and circle 2nd

Drawing another right triangle

We get

• leg = 3+3 - 2-1.5
• leg = 2.5 cm

Then, hypotenuse

• = 1.5 +2
• = 3.5 cm

Now again using Pythagorean theorem

Perpendicular = √6

∵ AB = √6 + 2√6

AB = 3√6

AB ≈ 7.35 cm  

So, the distance between AB is 7.35 cm