Mathematics
In the adjoining figure, if O is the centre of the circle then the value of x is
18°
20°
24°
36°
Circles
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Answer
From figure,
∠ADB = ∠ACB = 2x (∵ ∵ angles in same segment are equal.)
Join OA as shown in the figure below:
Arc AB subtends ∠AOB at centre and ∠ADB at remaining part of circle.
∠AOB = 2∠ADB = 2(2x) = 4x (∵ angle subtended at centre is double the angle subtended at remaining part of circle.)
In △OAB,
OA = OB (Radius of the circle.)
So, △OAB is an isosceles triangle with ∠OBA = ∠OAB (∵ angles opposite to equal sides are equal.)
∠OAB = 3x.
Since, sum of angles in a triangle = 180°.
⇒ ∠OAB + ∠OBA + ∠AOB = 180°
⇒ 3x + 3x + 4x = 180°
⇒ 10x = 180°
⇒ x = 18°
Hence, Option 1 is the correct option.
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