honors geometry

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A belt wrapped tightly around cicle O forms a 60 degree angle at P, a point outside the circle. Find the length of the belt if cicle O has a radius of 9.

  • honors geometry -

    That's kind of hard to imagine, but it seems to me you just plug 9 in into the formula... Please clarify if I'm wrong.

  • honors geometry -

    A belt wrapped tightly around cicle O forms a 60 degree angle at P, a point outside the cicle. Find the length of the belt if the cicle O has a radius of 9.
    diagram looks like a cicle with two tangent lines joining at point P outside the cicle. looks like a ice cream cone.
    need help

  • honors geometry -

    Lines from the points of contact of a tangent to the center of the circle are at right angles to the tangent.

    Draw triangles connecting a tangent point, P and the center of the circle. This will form two 30-60-90 right triangles.

    The angle subtended by the belt from the center of the circle is 120 degrees.

    The length of the belt is (2/3)*pi*R
    = 18.85

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