mathematics

an isosceles triangle ABC has its vertices on a circle.if /AB/=13CM,/BC/=13cm and /AC/=10CM,calculate the radius of the circle,to nearest whole cm

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  1. from diagram
    sin=5/13=0.3846
    =22.6
    now angle at center is twice the angle at any point of the circumference
    22.6*2=45.2
    sin45.2=5/r
    now find r

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  2. Place the circle in such a way that the midpoint of CA becomes the origin, and
    B lies on the y-axis
    by Pythagoras BO = 12 cm
    so we have points A(5,0), B(0,12) and C(-5,0)
    let the centre be (0,k) and the radius r
    equation:
    x^2 + (y-k)^2 = r^2

    using (5,0) --> 25 + k^2 = r^2
    using (0,12) -> 0 + (12-k)^2 = r^2
    12-k = r
    k = 12-r

    in 25+k^2 = r^2
    25 + (12-r)^2 = r^2
    25 + 144 - 24r + r^2 = r^2
    24r = 169
    r = 169/24 = 7.04166

    The radius is appr 7 cm

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  3. It is correct and good

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  4. Yes

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  5. Thanks but i mean using diagram

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  6. Explain it with diagram pls

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