Let the in circle to a Delta ABC touch BC AC and AB respectively at the points X Y and Z I If AB gt ...........

Quantitative Aptitude (CDS) Coordinate Geometry

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Let the in circle to a ΔABC touch BC, AC and AB respectively at the points X, Y and Z.

I: If AB > BC, then AB + AZ < BC + XC

II: AZ = AY Which one of the following is correct in respect of the above statements?

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

Statement I and 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

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Explanation:

In ΔAOZ and ΔAOY,
AO = OA [common]
$\angle$ OAZ = $\angle$ OAY [Since, OA bisects $\angle$ A]
and $\angle$ AZO = $\angle$ AYO [each 90°]
∴ Δ AZO ≅ AYO
So, AZ = AY [by CPCT]
Similarly, CX = CY and BX = BZ
Now, AB > BC
∴ AZ + ZB > BX + XC
AZ > XC [ $\because$ BX = XC]
If AB > BC, then AB + AZ > BC + XC
So, Statement I is incorrect and Statement II is correct.