Question

three circle of diameter 3cm ,4cm and 6cm are inscribed inside a rectangle with the middle circle touching the other two circles find the distance AB​

Answer 1

Given: r1 = 1.5  cm, r2 = 2 cm, r3 = 3 cm

To find: We have to find the horizontal distance between A and B

Solution:

• Let A be the point above the radius of circle 1.5 cm and B  be the point above the radius of circle 3 cm

• First consider the circle of radius 2 cm and 3 cm,

         perpendicular = 3 cm  -2 cm = 1 cm

         hypotenuse = 2 cm + 3 cm = 5 cm

• By using the pythagoras theorem, lets find the value of the base of the triangle.

          height² = perp² + base²

          perp² + 1² = 5²

          perp² = 25 - 1

          perp = √24

          perp = 2√6 cm

• Now, lets considering the circle of radius 1 cm and 2 cm by drawing another right triangle we get:

         perpendicular = 3 cm + 3 cm - 2 cm - 1.5 cm

         perpendicular = 2.5 cm

         then hypotenuse = 1.5 cm + 2cm = 3.5 cm

• Now by using pythagoras theorem, we get

          perpendicular = √6

          thus distance between the centre of the circle of radius 1.5 cm and 3 cm

          = √6 + 2√6

          = 3√6

          = 7.35 cm

Answer:

               The distance between the two circles is 7.35 cm