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
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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
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