Xavier Aptitude Test 2011 Paper

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DIRECTIONS (Qs. 52 and 53) : Given questions are followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

Question : 52 of 101

Marks: +1, -0

Let PQRS be a quadrilateral. Two circles O1 and O2 are inscribed in triangles PQR and PSR respectively. Circle O1 touches PR at M and circle O2 touches PR at N. Find the length of MN.
I. A circle is inscribed in the quadrilateral PQRS.
II. The radii of the circles O1 and O2 are 5 and 6 units respectively.

Statement I alone is sufficient to answer the question.
Statement II alone is sufficient to answer the question.
Statement I and Statement II together are sufficient, butneither of the two alone is sufficient to answer the question.
Either Statement I or Statement II alone is sufficient to answerthe question.
Neither Statement I nor Statement II is necessary to answerthe question.

Validate

Solution:

(b)
PD = a
QD = b
RM = c
PA = d
SA = e
PM = PA = PN + MN

QD = QC
RC = RN + RM
RM = RB
SA = SB
∴ PS = d + e
SR = e + c
QR = b + c + MN
PQ = a + b

Here,

\ {PQ}+\ {SR}=\ {PS}+ {QR}

x_{1}+x_{4}+x_{2}+x_{3}=x_{1}+x_{2}+x_{3}+x_{4}

\∴\ a+b+e+c=d+e+b+c+ {MN}

a=d+\ {MN}

\⇒\ a=d+\ {MN}+\ {MN}[\ ∵{PM}= {PA}]

⇒\ 2 {MN}=0

⇒\ {MN}=0

∴\

For MN only state I is sufficient

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