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Equation of the bisector of angle PQR for three given points

The same question, asked 2 times: 11 May 2023 S1*, 14 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    11 May 2023 S1

    146
    Let P≡(−5,0)P \equiv (-5,0), Q≡(0,0)Q \equiv (0,0) and R≡(2,23)R \equiv (2,2\sqrt{3}) be three points. Then the equation of the bisector of the angle PQR is

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  2. Question 2

    14 May 2024 S2

    143
    Let P(−3,0),Q(0,0)P(-3,0), Q(0,0) and R(3,33)R(3,3\sqrt{3}) be three points. Then the equation of the bisector of the angle PQR is

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