ONE
    Númas
    ← Back to the programme
    NationalMediumGeometry10–12

    Equation of a Circle and Position of a Point

    Equação de uma Circunferência e Posição de um Ponto

    In the plane, a circle has centre C(2, -1) and passes through the point A(6, 2). Write its equation and decide whether the point B(5, 3) lies inside the circle, on it, or outside it.

    The radius is not given, but the point known to lie on the circle determines it. To place B, compare its distance to the centre with that radius — no drawing is needed.

    Solution

    Step 1 of 4

    1. 1.r^{2} = (6 - 2)^{2} + (2 - (-1))^{2} = 16 + 9 = 25, so r = 5.