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CAT 2023 Question Paper | Quant Slot 1

CAT Previous Year Paper | CAT Quant Questions | Question 18

CAT 2023 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 18 : A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals

  1. 1 : 2
  2. 5 : 8
  3. 8 : 5
  4. 2 : 1

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Explanatory Answer

Quadrilateral inscribed in a circle.
DAC=DBC
(Angles subtended by the chord DC on the same side.)
ADB=ACB
(Angles subtended by the chord AB on the same side.)
AED=BEC
(Vertically Opposite angles.)

Therefore, AEDBEC
AEBE=EDEC=ADBC=45
ABD=ACD
(Angles subtended by the chord AD on the same side.)
BAC=BDC
(Angles subtended by the chord BC on the same side.)
AEB=DEC
(Vertically Opposite angles.)

Therefore, AEBDEC
AEED=BEEC=ABDC=21
AEED×EDEC=21×45=85
Therefore, AE : EC = 8 : 5


The question is " A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals "

Hence, the answer is '8 : 5'

Choice C is the correct answer.

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