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
∠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, △AED∼△BEC
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, △AEB∼△DEC
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 "
Choice C is the correct answer.
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