Multiple choice

In a circle with centre O and radius $5$cm, AB is a chord of length $5\sqrt 3$cm. Find the area of sector AOB.

  1. $\displaystyle\frac{25\pi}{2}cm^2$
  2. $\displaystyle\frac{23\pi}{3}cm^2$
  3. $\displaystyle\frac{25\pi}{7}cm^2$

  4. None of these
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D Correct answer
AI explanation

In triangle AOB, the radius is 5 cm and the chord AB is 5 times the square root of 3. By the cosine rule, the cosine of angle AOB equals (25 + 25 - 75) divided by 50, which is -0.5. The central angle is 120 degrees, so the sector area is (120/360) times pi times 25, resulting in an area of 25pi divided by 3. Therefore, the answer is none of these.

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