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26 April, 10:21

Find the circumcenter of the triangle ABC.

A ( - 4,3), B (5,7), C (-4,7).

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  1. 26 April, 10:48
    0
    Circumcenter O (0.5, 5)

    Step-by-step explanation:

    Circumcenter O (x, y)

    OA = OB = OC

    OA² = (x + 4) ² + (y - 3) ²

    OB² = (x - 5) ² + (y - 7) ²

    OC² = (x + 4) ² + (y - 7) ²

    OA² = OC² : (x + 4) ² + (y - 3) ² = (x + 4) ² + (y - 7) ²

    (y - 3) ² = (y - 7) ² y² - 6y + 9 = y² - 14y + 49

    8y = 40

    y = 5

    OB² = OC² : (x - 5) ² + (y - 7) ² = (x + 4) ² + (y - 7) ²

    x² - 10x + 25 = x² + 8x + 16

    18x = 9

    x = 0.5

    Circumcenter O (0.5, 5)
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