2014 · Q74
Let ABC be a triangle in which ∠ACB = 60° and AC = x < BC. Let the circle with centre at C and radius x meet BC at D. Let CF be the perpendicular drawn from C meeting AD at F.
Statement ITriangle ACD is isosceles but not equilateral.
Statement IIDF = x/2.
Which one of the following is correct in respect of the above statements?
Elementary MathematicsCircles
- AStatement-I and Statement-II are correct and Statement-II is the correct explanation of Statement-I
- BStatement-I and Statement-II are correct and Statement-II is not the correct explanation of Statement-I
- CStatement-I is correct and Statement-II is incorrect
- DStatement-I is incorrect and Statement-II is correct
Explanation
CA = CD = x with included angle 60° makes ACD equilateral (Statement-I false); the perpendicular from C bisects AD, so DF = x/2 (Statement-II true).