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

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#1

$Old$ May 17th, 2009, 07:27 PM

Mel $Mel is offline$

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$Default$ 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

$Old$ May 17th, 2009, 08:32 PM

Shyam $Shyam is offline$

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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,

$PO^2=PA^2+AO^2$

$PO^2=(24)^2+(7)^2$

$PO^2=576+49=625$

$PO=25$

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#3

$Old$ May 19th, 2009, 12:37 PM

HallsofIvy $HallsofIvy is offline$

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Originally Posted by Shyam $View Post$

Use Pythagorean Theorem,

$PO^2=PA^2+AO^2$

$PO^2=(24)^2+(7)^2$

$PO^2=576+49=625$

$PO=25$

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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