**power concept of a point of a circumference**allows relating the concepts studied in theorem

**Thales**and

**Pythagoras**and the door is to study problems such as tangents and transformations

**investment**.

**arc capable of a segment**at our shows, what is suggested by his review.

**product of two segments**and, but as we shall see adelante, to determine some important loci such as

**radical axis of two circles**.

## Definition of power

PowerWto a pointPon a circumferencecproduct is the most for the least distance from the pointPthe circumferencec.

The figure shows that the power point **P** respect to the circumference is **product segments** “**m**” and “**n**“, minimum and maximum distance from the point to the circumference. These segments are located on the diameter of the circle containing point **P**.

## Performance metrics Relations

We can relate metrically the basic concept of power on a circumference, using the Pythagorean theorem, tangency with the segment is obtained from the point to the circumference.

The power of a point

Pon a circumference is equal to the square difference between the distance from pointPcenterCthe circumference and the radiusRde la SMA; also the square of the segmentPTthe Tangente sayPis outside.

If we consider the segment “**m**” equals the distance “**d**” Point “**P**” center “**C**” the circumference “**c**“, minus the radius “**R**” de la SMA (**d-R**), and segment “**n**” is the sum of “**d**” and “**R**” (**d R**) we must:

As the sum of two times the difference variable is the difference of the squares, We see that the power “**W**” is equal to the difference of the squares of the distance “**d**” and the radius “**R**” the circumference. This expression reminds the leg of a right triangle, whose square is equal to the difference of squares of the hypotenuse and the other leg (side **the**).

If the point **P** is internal to the circumference of the segment not exist tangency, but we can also establish the relationship with the sides of a Pythagorean triangle.

The power of a point

Pon a circumference is equal to the difference of squares of the distance from pointPcenterCthe circumference and the radiusRthereof and also to the square of half chord segmentPTperpendicular aPCyouPis internal.

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