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Math Help - Distance from a point to the center of a circle

  1. #1
    Mel
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    Distance from a point to the center of a circle

    The length of tangent segment PA drawn from the exterior point P to circle O is 24. If the radius of the circle is 7, find the distance from point P to the center of the circle.
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  2. #2
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    Quote Originally Posted by Mel View Post
    The length of tangent segment PA drawn from the exterior point P to circle O is 24. If the radius of the circle is 7, find the distance from point P to the center of the circle.
    Use Pythagorean Theorem,

     <br />
PO^2=PA^2+AO^2<br />

     <br />
PO^2=(24)^2+(7)^2<br />

     <br />
PO^2=576+49=625<br />

     <br />
PO=25<br />
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  3. #3
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    Quote Originally Posted by Shyam View Post
    Use Pythagorean Theorem,

     <br />
PO^2=PA^2+AO^2<br />

     <br />
PO^2=(24)^2+(7)^2<br />

     <br />
PO^2=576+49=625<br />

     <br />
PO=25<br />
    Shyam's point is that, since a tangent to a circle is perpendicular to the radius at the point of tangency, the three lines form a right triangle. That is why the Pythagorean theorem can be used.
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