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Question
In following figure , chord ED is parallel to the diameter AC of the circle. Given ∠ CBE = 65° , calculate ∠DEC .
Solution
Let O be the centre of the cirde on diameter AC of the circle
Since, EC make ∠ EOC at the centre and ∠ EBC on the remaining part of the circle
∴ ∠ EOC = 2 ∠EBC = 2 (65) = 130°
In Δ EOC ,
∠EOC + ∠ OCE + ∠ CEO = 180°
130 + x + x = 180° (OE = OC , ∴ ∠ OEC = ∠ OCE = x)
2x = 50
x = 25
∠ OCE = ∠ OEC = 25°
Also , ∠ OCE = ∠ CED = 25° (alternate interior angles)
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