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Question
In the adjoining figure, TS is a tangent to a circle with centre O. The value of 2x° is ______.
Options
22.5
45
67.5
90
MCQ
Fill in the Blanks
Solution
In the adjoining figure, TS is a tangent to a circle with centre O. The value of 2x° is 45.
Explanation:
TS is a tangent to the circle at point S.
∠OST = x°
∠OSS = 3x° (since OS is the radius and meets the tangent at 90°).
We need to find the value of 2x°.
In ΔOST
∠OST + ∠OTS + ∠TOS = 180°
3x + x + 90 = 180
4x + 90 = 180
4x = 90
x = `90/4`
x = 22.5°
2x = 2 × 22.5
= 45°
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