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Triangle with a given angle bisector: reflect a vertex in the bisector

This type of question, asked 2 times: 2021 Paper 18, 29 Jan 2024. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 18

    79
    Let ABCABC be a triangle with A(−3,1)A( - 3,1) and ∠ACB=θ,0<θ<π2\angle ACB =\theta,0 <\theta<\frac{\pi}{2}. If the equation of the median through BB is 2x+y−3=02x + y - 3 = 0 and the equation of angle bisector of CC is 7x−4y−1=07x- 4y- 1 = 0, then tan⁡θ\tan\theta is equal to:

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  2. Question 2

    29 Jan 2024

    67
    In a △ABC\bigtriangleup ABC, suppose y=xy = x is the equation of the bisector of the angle BB and the equation of the side ACAC is 2x−y=22x - y = 2. If 2AB=BC2AB = BC and the point AA and B are respectively (4,6)(4,6) and (α,β)(\alpha,\beta), then α+2β\alpha + 2\beta is equal to

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