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CAT 2004 — QA Question 20

Simple EquationsEasy
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.

In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If ∠CBE = 65°, then what is the value of ∠DEC?

Answer & solution

  • A

    35°

  • B

    55°

  • C

    45°

  • 25°

Solution

m∠EBC = 65°

∴ m∠EOC = 130° (∵ angle subtended by an arc at the centre is twice the angle subtended by the same arc on the circumference)  

As AC || ED, m∠OCE = m∠DEC

ΔOEC is an isosceles triangle.

∴ m∠OCE = m∠OEC = (180 – 130)/2 = 25°

∴ m∠DEC = 25°

Hence, option (d).

CAT 2004 QA Q20: In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If ∠CBE = 65°, then wh — Solution | TheCATExam