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Let ABC be an equilateral triangle, with each side of length \(k\). If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is

Question and options

Let ABC be an equilateral triangle, with each side of length kk. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is
  1. (33+π)k224\left(3\sqrt{3} + \pi\right) \frac{k^2}{24}
  2. (33+π)k26\left(3\sqrt{3} + \pi\right) \frac{k^2}{6}
  3. (33−π)k224\left(3\sqrt{3} - \pi\right) \frac{k^2}{24}
  4. (33+π)k28\left(3\sqrt{3} + \pi\right) \frac{k^2}{8}

Answer and explanation

Correct answer: A - \(\left(3\sqrt{3} + \pi\right) \frac{k^2}{24}\)
Circle with diameter AB (centre O, radius k/2) passes through midpoints E of AC and F of BC (feet of altitudes). Inside region = triangles OAE and OBF (equilateral, side k/2) + 60-degree sector EOF: 2*(sqrt3/4)(k/2)^2 + (pi/6)(k/2)^2 = (3sqrt3+pi)k^2/24.

Practice for these exams

  • IPMAT Indore

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