Question

If A, B, C are the angles of a triangle and eⁱA, eⁱB, eⁱC are in A.P., then the triangle must be

• A. right angled
• B. isosceles
• C. equilateral
• D. None of these

Hint:

Equal angles in a triangle always imply an equilateral triangle.

Answer 1

The Correct Option is C

Step 1: If three quantities are in A.P., then: 2eⁱB = eⁱA + eⁱC Step 2: This condition implies symmetry about B, hence: A = B = C Step 3: A triangle with all equal angles is equilateral.