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Let ABC be a triangle in which ∠ACB = 60° and AC = x < BC. Let the circle with centre C and radius x meet BC at D. Let CF be the perpendicular from C meeting AD at F.

Statement—I: Triangle ACD is isosceles but not equilateral.

Statement—II: DF = x/2

Which one of the following is correct in respect of the above statements?

Mathematics 2014 CDS Elementary Mathematics 2014 CDS 2014

Options

Statement—I and Statement—II are correct and Statement—II is the correct explanation of Statement—I

Statement—I and Statement—II are correct and Statement—II is not the correct explanation of Statement—I

Statement—I is correct and Statement—II is incorrect

Statement—I is incorrect and Statement—II is correct