CAT 2004 — QA Question 20
Simple EquationsEasy
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
Correct answer: 25°
- A
35°
- B
55°
- C
45°
25°
Solution
m∠EBC = 65°
∴ m∠EOC = 130° (âµ 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).