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Area of an equilateral triangle is cm2 . A circle passes through the incentre of the triangle such that one side of the triangle is chord to the circle such that the other two sides of the triangle are tangent to the circle. Find the area of the circle. 
  • a)
    24π sq. cm
  • b)
    32π/3 sq. cm
  • c)
    16π sq. cm
  • d)
    12πsq. cm 
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Area of an equilateral triangle is cm2. A circle passes through the in...
I is the incentre => mzBIC = 120°
m(arc BDC) = 240° ... (Inscribed angle theorem)
So, m(arc BIC) = 120° => mzBOC = 120° Therefore, mZlOC = mzOIC = 60°
Thus, ΔIOC is an equilateral triangle.
ΔIEC is 30°-60°-90° triangle.
Let IO = IC = OC = r
∴ EC = (r√3) / 2
∴ AC = (r√3)
∴ (√3 / 4) x (r√3)2 = 8√3
r2 = 32/3
πr2 = 32π/3 
Hence, option 2.
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Community Answer
Area of an equilateral triangle is cm2. A circle passes through the in...
To find the area of an equilateral triangle, we need to know the length of one of its sides. However, in this case, we are only given the area which is 8. Therefore, it is not possible to determine the length of the sides or the area of the equilateral triangle with the given information.
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Area of an equilateral triangle is cm2. A circle passes through the incentre of the triangle such that one side of the triangle is chord to the circle such that the other two sides of the triangle are tangent to the circle. Find the area of the circle.a)24π sq. cmb)32π/3 sq. cmc)16πsq. cmd)12πsq. cmCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Area of an equilateral triangle is cm2. A circle passes through the incentre of the triangle such that one side of the triangle is chord to the circle such that the other two sides of the triangle are tangent to the circle. Find the area of the circle.a)24π sq. cmb)32π/3 sq. cmc)16πsq. cmd)12πsq. cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Area of an equilateral triangle is cm2. A circle passes through the incentre of the triangle such that one side of the triangle is chord to the circle such that the other two sides of the triangle are tangent to the circle. Find the area of the circle.a)24π sq. cmb)32π/3 sq. cmc)16πsq. cmd)12πsq. cmCorrect answer is option 'B'. Can you explain this answer?.
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