Question

In the adjoining figure, TS is a tangent to a circle with centre O. The value of $2x^\circ$ is

• A. 22.5
• B. 45
• C. 67.5
• D. 90

Hint:

When tangents and radii form right triangles, use angle sum property to deduce unknowns.

Answer 1

The Correct Option is B

Given:
TS is a tangent to the circle at point S, and O is the center of the circle.
Angle at O is marked as \(90^\circ\) (since the radius is perpendicular to the tangent at the point of contact).
Angle ∠SOT = 90°, ∠OST = x°, ∠OTS = 3x°

Step 1: Use Triangle Angle Sum Property
In triangle OST:
\[ \angle SOT + \angle OST + \angle OTS = 180^\circ \]
\[ 90^\circ + x^\circ + 3x^\circ = 180^\circ \Rightarrow 90^\circ + 4x^\circ = 180^\circ \Rightarrow 4x = 90 \Rightarrow x = 22.5^\circ \]

Step 2: Find the value of \(2x\)
\[ 2x = 2 \times 22.5^\circ = 45^\circ \]

Final Answer:
The value of \(2x^\circ\) is 45°.