Mathematics
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°
Answer
From figure,
MQ is chord and XQY is a tangent.
∠P = ∠MQY (∵ angles in alternate segment are equal.)
As PM || XQY
∠MQY = ∠M (∵ alternate angles are equal)
∴ ∠P = ∠M = 70°
We know that sum of angles in a triangle = 180°.
In △PQM,
⇒ ∠P + ∠M + ∠PQM = 180°
⇒ 70° + 70° + ∠PQM = 180°
⇒ 140° + ∠PQM = 180°
⇒ ∠PQM = 180° - 140°
⇒ ∠PQM = 40°.
Hence, option 3 is the correct option.
Related Questions
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 figure, XY is a tangent at X to the circle with centre O. If ∠XYO = 25°, then x = ?
25°
115°
65°
60°
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
Assertion (A): From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn, then the radius of the circle is 5 cm.
Reason (R): In a circle, radius through the point of contact is perpendicular to the tangent.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false