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A cyclic quadrilateral ABCD is drawn in a circle with centre...

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Geometry
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A cyclic quadrilateral ABCD is drawn in a circle with centre O. A and C are joined to O. If ∠ABC = 2p and ∠ADC = 3p, what is the measure (in degrees) of the ∠AOC reflex?

Answer & Solution
Correct Answer: Option D
Geometry mcq question image
ABCD is cyclic quadrilateral
∴ 3p + 2p = 180°
5p = 180°
p = 36°
∠ADC = 3p = 3 × 36 = 108°
∠AOC = $$\frac{1}{2}$$∠ADC
= $$\frac{1}{2}$$ × 108°
= 54°
Reflex of ∠AOC = 360° - 54° = 206°
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