# CAT 2018 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Geometry Questions | Question 4

It is almost a no-brainer that CAT Geometry must be mastered, and there's no escaping this topic in you online CAT Preparation. Over the years, the Geometry has been given huge emphasis, which makes it the second most important topic after Arithmetic. Visit 2IIM's CAT Blueprint to know more about what to expect in the upcoming CAT exam. Solve this question from CAT Previous Year Paper 2018 and ace your preparation.

Question 4 : On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is [TITA]

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##### Method of solving this CAT Question from Geometry

Let ABC be the triangle on which a circle of diameter BC is drawn, intersecting AB and AC at points P and Q respectively.The lengths of AB ,AC and CP are 30cm , 25cm and 20 cm respectively we have to find the length of BQ in cm.
Key thing here is ,this is semicircle so this angle P and Q should be 90° and now we are looking to do Pythagoras theorem

So think about triangle PAC, by Pythagoras theorem
AC2 = AP2 + PC2 we can find that AP = 15

Since AP = 15 we can find BP by
AB = AP + PB
30 = 15 + PB
PB = 15
Now we can look at the triangle BPC, by Pythagoras theorem we can find that BC = 25

Now we have to find BQ .So we can take the area of the triangle formula which is equal to $$frac{1}{2}$ × base × height area of the triangle formula = $\frac{1}{2}$ × base × height $\frac{1}{2}$ × AB × PC = $\frac{1}{2}$ × AC × BQ $\frac{1}{2}$ × 30 × 20 = $\frac{1}{2}$ × 25 × BQ BQ = 24 cm The question is "On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is [TITA] " ##### Hence, the answer is 24 cm ###### Prepare for CAT 2023 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ##### 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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