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Let O be the center of the circle Γ, and P be a point outside of circle Γ. PA is tangential to Γ at A, and PO intersects Γ at D. If PD=14 and PA=42, what is the radius of Γ.

  • geometry - ,

    In this case the secant - tangent theorem says

    PA^2 = PD x PC , where D in on the extension of PO as it hits the circle , making CD a diameter
    Let the diameter be 2x , (radius = x)
    (14)(2x+14) = 42^2
    28x + 196 = 1764
    28x = 1568
    x = 56

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