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Given that S₁ = x, which refers to TSP = x.

April 13, 2026Mathematics

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$\angle O_1$

Express, giving reasons, each of the following angles in terms of $x$ .

Given that $S_1 = x$ , which refers to $\angle TSP = x$ .

Identify $\angle O_1$ .
From the diagram, $\angle O_1$ is $\angle SOT$ . This is the angle subtended by arc ST at the center.
Relate $\angle SOT$ to an angle at the circumference.
The angle subtended by arc ST at the circumference is $\angle SPT$ .
The angle at the center is twice the angle at the circumference subtended by the same arc.

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