Complete the following theorem statement: Angles subtended by a chord of the circle, on the same side of the chord … In the diagram below, circle PTRS, with centre O, is given such that PS = TS - NSC Technical Mathematics - Question 7 - 2021 - Paper 2

To determine the size of ∠P₁, we first recognize that ∠PSR = 90° since it is inscribed in a semicircle. Therefore:

1. The triangle formed by points P, S, and R gives:

   $\angle P₁ + 90° + 56° = 180°$

2. Rearranging gives:

   $\angle P₁ = 180° - 90° - 56° = 34°$

To find the size of ∠S₃, we can use the fact that angles inscribed in the same segment are equal:

1. Also, knowing that

   $\angle S₁ + \angle S₂ + \angle S₃ = 90°$

2. Thus:

   $\angle S₃ = 180° - (90° + 34°) = 56°$

To show that OT is not parallel to SR, we can use the following reasoning:

1. At the center O,

   $\angle O_T = 112°$ (because the angles are formed at the center by the same arc)

2. Also, at the radius points:

   $\angle O₁ = 44°$

3. Since the sum of the angles is not equal to 180°, we arrive at:

   $OT is not parallel to SR$ (as alternate angles do not equal each other).