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प्रश्न
In the given diagram, PS and PT are the tangents to the circle. SQ || PT and ∠SPT = 80°. The value of ∠QST is ______.
विकल्प
140°
90°
80°
50°
उत्तर
In the given diagram, PS and PT are the tangents to the circle. SQ || PT and ∠SPT = 80°. The value of ∠QST is 50°.
Explanation:
PS and PT are tangents from an exterior point to a circle from point P
i.e., PS = PT
So ∠PST = ∠PTS
In ΔPST,
∠PST + ∠PTS + ∠SPT = 180°
2∠PTS = 180° – 80° = 100°
∠PTS = 50°
Here, SQ || PT and ST is a transversal
Then, ∠QST = ∠STP = 50° ...(Alternate pair of angles)
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