# Distance from a point to the center of a circle

• 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,

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

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

$
PO^2=576+49=625
$

$
PO=25
$
• May 19th 2009, 10:37 AM
HallsofIvy
Quote:

Originally Posted by Shyam
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.