# Thread: Distance from a point to the center of a circle

1. ## 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.

2. 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,

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

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

$\displaystyle PO^2=576+49=625$

$\displaystyle PO=25$

3. Originally Posted by Shyam
Use Pythagorean Theorem,

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

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

$\displaystyle PO^2=576+49=625$

$\displaystyle PO=25$
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.