Mathematics
In the figure, XY is a tangent at X to the circle with centre O. If ∠XYO = 25°, then x = ?
25°
115°
65°
60°
Answer
∠XYO = 25°
In a circle, radius through the point of contact is perpendicular to the tangent.
∠OXY = 90°
In △ XOY,
By angle sum property of triangle,
⇒ ∠XYO + ∠OXY + ∠XOY = 180°
⇒ 25° + 90° + ∠XOY = 180°
⇒ ∠XOY + 115° = 180°
⇒ ∠XOY = 180° - 115° = 65°.
From figure,
∠XOY + x = 180° [Linear pairs]
x = 180° - 65°
x = 115°.
Hence, option 2 is the correct option.
Related Questions
In the given figure, RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60°, then ∠PSQ is :
40°
30°
60°
90°
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°
In the given figure, XQY is a tangent at Q to a circle. If PM is a chord parallel to XY and ∠MQY = 70°, then ∠PQM = ?
20°
35°
40°
70°
Assertion (A): In the figure, AB, AC and DE are tangents to the circle. If AC = 7 cm, then perimeter of ΔADE is 14 cm.
Reason (R): The lengths of tangents to a circle from an exterior point are equal.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
