In a circle with centre O, AC and Bd are two chords. AC and BD meet at E., wen produced . If AB is a diameter and ∠AEB = 36°, then te measure of∠DOC is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 108°
In the given figure, OA = OB = OC = OD = Radius of the circle = r
Triangle(AOC) and triangle(BOD) are isosceles triangles.
Thus, let ∠OAC and ∠ACO = x and ∠DBO and ∠BDO also x°
In triangle(AEB), 2x + 36 = 180
⇒ 2x = 144 ⇒ x = 72
∠ACO + ∠ECO = 180 (Linear Pair)
⇒ ∠ECO = 180 - 72 = 108°
Similarly, ∠EDO = 108°
Figure ECOD is quadrilateral.
Sum of all the angles = 360°
∠COD + ∠ECO + ∠EDO + ∠CED = 360
⇒ ∠COD + 108 + 108 + 36 = 360
⇒ ∠COD + 252 = 360
⇒ ∠COD = 360 - 252 = 108°