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CAT 2004 — QA Question 21

Basics of CirclesEasy
Passage / Data

Answer the following question based on the information given below.

In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4 : 3. It is also known that the length of PO is 28 cm.

On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has length 2, while AD has length 8. What is the length of BC?

Answer & solution

  • A

    7.5

  • 7

  • C

    7.75

  • D

    None of the above

Solution

Quadrilateral ABCD is an isosceles trapezium. Let AM = DN = x

∵ AD = 8, AO = DO = BO = 4

∴ OM = ON = 4 – x

ΔBMO and ΔBMA are right triangles.

∴ OB2 = OM2 + MB2

∴ 16 = (4 – x)2 + h2         …(i)

Also,

AB2 = MB2 + AM2

4 = x2 + h2                      …(ii)

From (i) and (ii), x = 0.5

∴ BC = 2(4 – x)

∴ BC = 7

Hence, option (b).

CAT 2004 QA Q21: On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD — Solution | TheCATExam