2014 · Q73
Let the incircle to a triangle ABC touch BC, AC and AB respectively at the points X, Y and Z.
Statement IIf AB > BC, then AB + AZ < BC + XC.
Statement IIAZ = AY.
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
Tangents from a vertex are equal (AZ = AY), but AB + AZ vs BC + XC: with AZ = AY, BX = BZ, CX = CY, AB > BC gives AB + AZ > BC + XC, so Statement-I is false.