# CAT 2023 Question Paper | Quant Slot 2

###### 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 triangle is drawn with its vertices on the circle $C$ such that one of its sides is a diameter of $C$ and the other two sides have their lengths in the ratio $a: b$. If the radius of the circle is $r$, then the area of the triangle is

1. $$frac{a b r^2}{2$left$a^2+b^2$right$}$ 2. $$frac{a b r^2}{a^2+b^2}$ 3. $\frac{4 a b r^2}{a^2+b^2}$ 4. $\frac{2 a b r^2}{a^2+b^2}$ ## 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 Since the angle subtended by the diameter on the circle is a right-angle, such a triangle inscribed in a circle with the diameter as one of its sides will be right angled. “…and the other two sides have their lengths in the ratio a: b.” Let the two sides be ax and bx. The area of the triangle = $\frac { 1 } { 2 } \times a x \times b x = \frac { a b } { 2 } x ^ { 2 }$ By the Pythagoras theorem, $$ a x$ ^ { 2 } + ( b x ) ^ { 2 } = ( 2 r ) ^ { 2 }$
$$left$ a ^ { 2 } + b ^ { 2 } $right) $times x ^ { 2 } = 4 r ^ { 2 }$ $x ^ { 2 } = \frac { 4 r ^ { 2 } } { \left$ a ^ { 2 } + b ^ { 2 } $right$ }$ ∴The area of the triangle $= $frac { a b } { 2 } \times \frac { 4 r ^ { 2 } } { \left$ a ^ { 2 } + b ^ { 2 } $right$ } = $frac { 2 a b r ^ { 2 } } { a ^ { 2 } + b ^ { 2 } }$ The question is " A triangle is drawn with its vertices on the circle $C$ such that one of its sides is a diameter of $C$ and the other two sides have their lengths in the ratio $a: b$. If the radius of the circle is $r$, then the area of the triangle is " ##### The answer is '$\frac{2 a b r^2}{a^2+b^2}$' Choice D 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
WhatsApp: WhatsApp Now
Email: info@2iim.com