CAT 2018 Question Paper | Quants Slot 2

The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. If you would like to take the same inside a testing engine (for Free) head out here: CAT Official Question Mocks. In CAT 2018 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank

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]

Video Explanation

Explanatory Answer

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