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Two tangents XY and XZ are drawn from a point X to a circle with center W.If the length of XZ is 156 and the length YZ is 120,find the radius of the circle.

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  1. I assume you know the properties of tangents with circles.
    Join XW and YZ, label their intersection point V
    XW bisects angle X, and XW right-bisects YZ
    Label angle WXZ as Ø
    sinØ = 60/158 = 30/7
    Ø = sin^-1 (30/79)

    Join WZ, where WZ is the radius and we have another right angle at Z this time
    tanØ = WZ/156
    WZ =156 tan Ø
    = 156 tan (sin^-1 (30/79) )
    = appr 64.04

    check my calculations

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