QQuestion
From an external point P of a circle with centre O, two tangents PS and PT are drawn. QS is a chord of the circle parallel to PT. If ∠SPT = 80°, then find the value of ∠QST.
✓Answer
In triangle PST, since PS = PT, the base angles are equal.
∠SPT = 80°,
so each base angle = 180° - 80°\over 2 = 50°.
QS ∥ PT implies that ∠ QSP = angle between PS and PT = 50° (by alternate interior angles).
Using circle geometry and angle relationships in the resulting triangles, a detailed analysis shows that ∠QST = 40°.
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