Mathematics
In the given circle with diameter AB, find the value of x.
Circles
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Answer
As angles in same segment are equal.
∴ ∠ABD = ∠ACD = 30°.
From figure,
∠ADB = 90° [As angle in semi-circle is a right angle.]
In △ADB,
⇒ ∠ABD + ∠ADB + ∠BAD = 180° [By angle sum property of triangle]
⇒ 30° + 90° + x = 180°
⇒ 120° + x = 180°
⇒ x = 180° - 120° = 60°.
Hence, the value of x = 60°.
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O is the center of the circle, OB = BC and ∠BOC = 20°.
Statement (1) : x = 2 x 20° = 40°
Statement (2) : ∠BOC = 20°.
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O is the center of the circle and ∠AOC = 120°.
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