Mathematics
In the given figure, PT and QT are tangents to a circle such that ∠TPS = 45° and ∠TQS = 30°. Then, the value of x is :
30°
45°
75°
105°

Circles
34 Likes
Answer
We know that,
The angle between a tangent and a chord through point of contact is equal to an angle in the alternate segment.
∴ ∠SQP = ∠SPT = 45° and ∠SPQ = ∠SQT = 30°.
In △ SQP,
⇒ ∠SQP + ∠SPQ + ∠QSP = 180°
⇒ 45° + 30° + ∠QSP = 180°
⇒ 75° + ∠QSP = 180°
⇒ ∠QSP (x) = 180° - 75° = 105°.
Hence, Option 4 is the correct option.
Answered By
22 Likes
Related Questions
In the adjoining figure, O is the center of the circle, and a semicircle is drawn on OA as the diameter. ∠APQ = 20°. The degree measure of ∠OAQ is :
25°
40°
50°
65°

In the given diagram, O is the center of the circle, and PQ is a tangent at A. If ∠ABC = 50°, then values of x, y and z respectively are :
50°, 100°, 40°
50°, 50°, 65°
40°, 80°, 50°
50°, 25°, 78°

A cylindrical metallic wire is stretched to double its length. Which of the following will NOT change for the wire after stretching?
Its curved surface area
Its total surface area
Its volume
Its radius
A right circular cone has the radius of the base equal to the height of the cone. If the volume of the cone is 9702 cu. cm, then the diameter of the base of the cone is :
21 cm
42 cm
cm
cm