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 .find the distance between ab .
Answers
Answer:
Answer will be 3√6
The distance between AB is 7.35 cm
Step-by-step explanation:
radius of 1st circle = 1.5 cm
radius of second circle = 2 cm
radius of third circle = 3 cm
we have to find the horizontal distance between A and B
considering circle 2 and 3
leg = 3-2 = 1 cm
hypotenuese = 2+3 = 5 cm
using the pythagoras theorem we find the other leg of perpendicular
h² = p² + b²
5² = p² + 1²
p² = 25-1
p =√24
p = 2√6 cm
now considering circle 1 and 2
drawing another right triangle
we get
leg = 3+3 - 2-1.5
leg = 2.5 cm
then hypotenuese = 1.5+ 2= 3.5 cm
now again usig pythagoras theorem
perpendicular = √6
thus AB = √6 + 2√6
AB = 3√6
AB = 7.35 cm approximately
hence , The distance between AB is 7.35 cm
#Learn more :
A rectangle with one side 4 cm is inscribed in a circle of diameter 5 cm. Find the area of rectangle
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