In the given figure, ABC is an equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side (in cm) of an equilateral triangle ?
A) 32/√3 B) 32√3 C) 64/√3 D) None
Answers
Given : ABC is equilateral triangle.
Two circles of radius 4 cm and 12 cm are inscribed in the triangle.
To Find : What is the side of equilateral triangle
A) 32/√3 B) 32√3 C) 64/√3 D) None
Solution:
Let say side of equilateral triangle = a
Area of equilateral triangle = (√3 / 4) a²
Area of triangle = semi perimeter of triangle * inradius
in radius = 12 cm ( radius of larger circle )
semi perimeter = (a + a + a)/2 = 3a/2
Area of triangle = (3a/2) * 12 = 18a
(√3 / 4) a² = 18a
=> a² = 72a /√3
=> a = 72 /√3
=> a = 24√3
side of equilateral triangle = 24√3
None is the correct option
Note : There is no importance of smaller circle
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