Mathematics
In the given figure, O is the centre of the circle and AB is a chord. If the tangent AM at A makes an angle of 50° with AB, then ∠AOB = ?
100°
75°
80°
150°
Answer
In a circle, radius through the point of contact is perpendicular to the tangent.
∠OAM = 90°
∠OAB + ∠BAM = 90°
∠OAB + 50° = 90°
∠OAB = 90° - 50°
∠OAB = 40°
OA = OB (Radii of same circle)
∠OBA = ∠OAB = 40° [Angles opposite to equal sides in a triangle are equal]
In △AOB,
By angle sum property of triangle,
⇒ ∠OBA + ∠OAB + ∠AOB = 180°
⇒ 40° + 40° + ∠AOB = 180°
⇒ ∠AOB + 80° = 180°
⇒ ∠AOB = 180° - 80° = 100°.
Hence, option 1 is the correct option.
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