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PEM Level C
12 December 2009
Topics in Geometry  The Power Theorems, Power of a Point
Theorems:
1. (Power Theorem)
Let
P
be a given point, and let
‘
be a line that passes through
P
and
intersecting a given circle at two (not necessarily distinct) points
A
and
B
. Then the product
PA
·
PB
is constant for any choice of the line
‘
.
2. (TwoChord Power Theorem)
Let
P
be a point inside a circle. Let
‘
1
and
‘
2
be two chords of
the circle that intersect at
P
. Let
A
1
and
B
1
be the endpoints of
‘
1
, and let
A
2
and
B
2
be the
endpoints of
‘
2
. Then
PA
1
·
PB
1
=
PA
2
·
PB
2
.
3. (TwoTangent Power Theorem)
Let
P
be a point outside a circle. Let
‘
1
and
‘
2
be the two
tangents to the circle through
P
. Let
T
1
and
T
2
be the points of tangency of
‘
1
and
‘
2
,
respectively, to the circle. Then
PT
1
=
PT
2
.
4. (TangentSecant Power Theorem)
Let
P
be a point outside a circle. Let
‘
1
be a tangent to
the circle through
P
, and
‘
2
a secant to the circle through
P
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This note was uploaded on 11/15/2010 for the course MATH 100 taught by Professor B during the Spring '09 term at Ateneo de Manila University.
 Spring '09
 B
 Geometry

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