Distance from a point to the center of a circle

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May 17th 2009, 05:27 PM
Mel

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.
May 17th 2009, 06:32 PM
Shyam

Quote:

Originally Posted by Mel

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,

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

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

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

$<br /> PO=25<br />$
May 19th 2009, 10:37 AM
HallsofIvy

Quote:

Originally Posted by Shyam

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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