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Geometry Practice : Triangle Properties

This aptitude practice question is a geometry question that tests your understanding of trigonometric ratios and sin rule. This one is a medium level difficulty question.

Question

If in a triangle ABC, \\frac{cos A}{a}) = \\frac{cos B}{b}) = \\frac{cos C}{c}), then what can be said about the triangle?

  1. Right angled triangle
  2. Isosceles triangle
  3. Equilateral triangle
  4. Nothing can be inferred

  Correct Answer      Choice (C). Equilateral triangle


Explanatory Answer

From the sine rule of triangles we know \\frac{a}{sin A}) = \\frac{b}{sin B}) = \\frac{c}{sin C}) = k

Therefore, a = k(Sin A), b = k(Sin B) and c = k(Sin C)

Hence, we can rewrite \\frac{cos A}{a}) = \\frac{cos B}{b}) = \\frac{cos C}{c}) as \\frac{cos A}{kSin A}) = \\frac{cos A}{kSin B}) = \\frac{cos A}{kSin C})

Or Cot A = Cot B = Cot C
Or A = B = C
Or the triangle is an equilateral triangle

  The correct answer is Choice (C).

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