# CAT 2023 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 17

CAT 2023 Quant was dominated by Arithmetic followed by Algebra. 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 17 : Let $$triangle A B C$ be an isosceles triangle such that $A B$ and $A C$ are of equal length. $A D$ is the altitude from $A$ on $B C$ and $B E$ is the altitude from $$mathrm{B}$ on $\mathrm{AC}$. If $\mathrm{AD}$ and $\mathrm{BE}$ intersect at $\mathrm{O}$ such that $\angle \mathrm{AOB}=105^{\circ}$, then $\frac{A D}{B E}$ equals 1. $2 \sin 15^{\circ}$ 2. $\cos 15^{\circ}$ 3. $2 \cos 15^{\circ}$ 4. $\sin 15^{\circ}$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer Area of triangle ABC = $\frac { 1 } { 2 } \times A D \times B C = \frac { 1 } { 2 } \times B \in \times A C$ $\frac { A D } { B E } = \frac { A C } { B C }$ $\angle B O A + \angle A O E = 180 ^ { \circ } \quad$ B E$ is a straight line $$$
$$angle A O E = 75 ^ { $circ }$ $\angle A O E + \angle O A E + \angle A E O = 180 ^ { \circ }$$Sum of internal angles of a triangle$
$$angle O A E = 15 ^ { $circ }$ Since $\triangle B O D \cong \triangle A O E , \angle O B D = 15 ^ { \circ }$ $\angle B C A = \angle B C E = 180 ^ { \circ } -$ $angle E B C + \angle B E C$ = 75 ^ { $circ }$ By symmetry, $\angle A B D = \angle B C A = 75 ^ { \circ }$ $\Rightarrow \angle A B C = 75 ^ { \circ } - 15 ^ { \circ } = 60 ^ { \circ }$ In $\triangle A B E$, $B E = A B \times \cos \cos \left$ 60 ^ { $circ } \right$$ In $$triangle B E C$, $B E = B C \times \cos \cos \left$ 15 ^ { $circ } \right$$ $A B $times \cos \cos \left$ 60 ^ { $circ } \right$ = B C $cos \cos \left$ 15 ^ { $circ } \right$$ Since AB = AC, $$frac { A C } { B C } = \frac { \cos \cos \left$ 15 ^ { $circ } \right$ } { $cos \cos \left$ 60 ^ { $circ } \right$ } = 2 $cos \cos \left$ 15 ^ { $circ } \right$$ The question is " Let $$triangle A B C$ be an isosceles triangle such that $A B$ and $A C$ are of equal length. $A D$ is the altitude from $A$ on $B C$ and $B E$ is the altitude from $\mathrm{B}$ on $\mathrm{AC}$. If $\mathrm{AD}$ and $\mathrm{BE}$ intersect at $\mathrm{O}$ such that $\angle \mathrm{AOB}=105^{\circ}$, then $\frac{A D}{B E}$ equals " ##### The answer is '$2 \cos 15^{\circ}$' Choice C is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## CAT Questions | Verbal Ability for CAT ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91$ 99626 48484 / 94459 38484
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