# 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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