Three circles of radii 3, 5, and 8 centimeters are mutually tangent. Find the area enclosed between the circles.

albiguguiismx

albiguguiismx

Answered question

2022-09-05

Three circles of radii 3, 5, and 8 centimeters are mutually tangent. Find the area enclosed between the circles.

Answer & Explanation

letovanjelm

letovanjelm

Beginner2022-09-06Added 13 answers

length of radii are 3, 5 and 8 cm
length of the sides of the traingle are the sum of respective radii:
let the sides of the traingle be a, b and c.
then,
a = 3 + 5 = 8   c m b = 5 + 8 = 13   c m c = 3 + 8 = 11   c m
Area of traingle = s ( s a ) ( s b ) ( s c )
here
s = a + b + c 2 s = 8 + 13 + 11 2 s = 16
therefore
Area (A) = s ( s a ) ( s b ) ( s c ) A = 16 ( 16 8 ) ( 16 11 ) ( 16 13 ) A = 16 ( 8 ) ( 5 ) ( 3 ) A = 4 2 30 A = 8 30 A = 43.82   c m 2

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