Mathematics
O is center of the the circle and ∠AOB = 60°. The length of chord AB is :
equal to radius of the circle
equal to the side of a regular pentagon
bigger than the radius of the circle
smaller than the radius of the circle.
Constructions
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Answer
From figure,
⇒ OA = OB (Radius of same circle)
⇒ ∠OBA = ∠OAB = x (let) [In a triangle angles opposite to equal sides are equal.]
In △ AOB,
By angle sum property of triangle,
⇒ ∠OBA + ∠OAB + ∠AOB = 180°
⇒ x + x + 60° = 180°
⇒ 2x + 60° = 180°
⇒ 2x = 180° - 60°
⇒ 2x = 120°
⇒ x = = 60°
⇒ ∠OBA = ∠OAB = ∠AOB = 60°.
∴ AOB is an equilateral triangle.
∴ AB = OA = OB
∴ AB = Radius of circle.
Hence, Option 1 is the correct option.
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