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      Question

      PQ is a tangent to the circle at T. If TR = TS where R

      and S are points on the circle and ∠ RST = 65°, the ∠ PTS = ?
      A 65° Correct Answer Incorrect Answer
      B 130° Correct Answer Incorrect Answer
      C 115° Correct Answer Incorrect Answer
      D 55° Correct Answer Incorrect Answer

      Solution

      ATQ, ∠SRT = ∠TSR = 65° [TR = TS] Now, ∠SRT + ∠TSR + ∠STR = 180° ∠STR = 180° - 65° - 65° = 50° ∠PTR = ∠STQ = 130°/2 = 65° ∴ ∠PTS = 65° + 50° = 115°

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