Q87 / 160 · TS EAMCET 2011 · Mathematics

In a $\triangle A B C$, if $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$, then $\triangle A B C$ is

  • A
    right angled
  • B
    isosceles right angled
  • Correct answer
    C
    equilateral
  • D
    scalene

Solution

$\text { In } \triangle A B C, \frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$ By sine rule, $\begin{array}{lc} \Rightarrow & \frac{\cos A}{k \sin A}=\frac{\cos B}{k \sin B}=\frac{\cos C}{k \sin C} \\ \Rightarrow & \cot A=\cot B=\cot C \\ \Rightarrow & A=B=C \end{array}$ Hence, all angles are equal so the $\triangle A B C$ is an equilateral.

Hence, the correct answer is option: 'C'.

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