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Question
If PQ is a tangent to the circle at R; calculate:
- ∠PRS,
- ∠ROT.
Given O is the centre of the circle and angle TRQ = 30°.
Solution
PQ is a tangent and OR is the radius.
∴ OR ⊥ PQ
∴ ∠ORT = 90°
`=>` ∠TRQ = 90° – 30° = 60°
But in ΔOTR,
OT = OR ...(Radii of the same circle)
∴ ∠OTR = 60° Or ∠STR = 60°
But,
∠PRS = ∠STR = 60 ...(Angle in the alternate segment)
In ΔORT,
∠ORT = 60°
∠OTR = 60°
∴ ∠ROT = 180° – (60° + 60°)
∴ ∠ROT = 180° – 120° = 60°
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