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CAT 1997 — QA Question 42

Basics of CirclesEasy
Passage / Data

Direction: Answer the questions based on the following information.

Boston is 4 hr ahead of Frankfurt and 2 hr behind India. X leaves Frankfurt at 6 p.m. on Friday and reaches Boston the next day. After waiting there for 2 hr, he leaves exactly at noon and reaches India at 1 a.m. On his return journey, he takes the same route as before, but halts at Boston for 1hr less than his previous halt there. He then proceeds to Frankfurt.

In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the area of Δ CBE to that of Δ ADE?

Answer & solution

  • 1 : 4

  • B

    1 : 2

  • C

    1 : 3

  • D

    Data insufficient

Solution

In ΔBEC and ΔAED

∠CBE = ∠CDE (angles in the same segment of a circle are equal)
Similarly ∠BCE = ∠EAD (angles in the same segment of a circle are equal)
∠BEC = ∠AED (Vertical angles are equal) 

∴ By AAA similarity 
ΔCEB ~ ΔAED
We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the
corresponding sides

∴ area(∆BEC)area (∆AED)=(BCDA)2=(1224)2=(12)2=14

CAT 1997 QA Q42: In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the — Solution | TheCATExam