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4 March, 06:23

The perpendicular bisector of chord AB is y=-2x+8, and the perpendicular bisector of chord BC is y = 3x-2. Recall the properties of chords. How can these equations be used to find the center of the circle that represents the whole plate

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  1. 4 March, 08:51
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    We equate the two expressions since they both pass through the center of the circle.

    The coordinate of the center of the circle is (2,4)

    Step-by-step explanation:

    From circle theorem, we know that the perpendicular bisector of a chord passes through the center of the circle.

    Since both equations would pass through the center of the circle, we equate them.

    So, - 2x+8 = 3x-2

    Solving for x, we have

    3x + 2x = 8 + 2

    5x = 10

    x = 10/5

    x = 2

    Substituting x = 2 into any of the equations, we find the y - coordinate of the center of the circle.

    y = - 2x + 8 = - 2 (2) + 8 = - 4 + 8 = 4

    So, the coordinate of the center of the circle is (2,4)
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