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From the diagram above. ABC is a triangle inscribed in a circle center O. ∠ACB...

Mathematics
WAEC 1999

From the diagram above. ABC is a triangle inscribed in a circle center O. ∠ACB = 40º and |AB| = x cm. Calculate the radius of the circle.

  • A. \(\frac{x}{sin 40^o}\)
  • B. \(\frac{x}{cos 40^o}\)
  • C. \(\frac{x}{2 sin 40^o}\)
  • D. \(\frac{x}{2 cos 40^o}\)
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Correct Answer: Option C
Explanation

In the diagram given in the question, < ABC = 90º ( < in a semi-circle)

In triangle ABC, Sin 40º = \(\frac{x}{|AC|}\) 

|AC| =  \(\frac{x}{sin40º}\) 

Since |AC| is a diameter, radius is half of |AC| =  \(\frac{x}{2sin40º}\)


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