teorema pytagoras menggunakan pembuktian irisan 2 lingkaran

1. PHYTAGOREAN THEOREM
#22
The Second Proof
From
Dr. Scott Brodie's
Presented by:
Kokom Komariah
102151022
4A

2. Dr. Scott Brodie’s take as known a "power of the point"
Power Of Point Theorem
( Jacob Steiner 1826)
Given circle O,
point P not on the circle,
and a line
through P intersecting the
circle in two points.
The product of the length
from P to the first point of
intersection
and the length from P to the
second point of intersection
is constant for any choice of
a line through P that intersects
the circle.
In 1826, Jacob Steiner used the word "power" to refer to the relationship
of a point to two intersecting lines and a circle.
Power of a Point Theorem
PA
C
D
B
PA . PB = PC . PD = the constant
1. theorem of intersecting secants.

3. 2. Theorem Of Intersecting Chords.
A
B
C
D
P
PA . PB = PC.PD = the constant
3. Secant Tangent theorem.
A
B P
C
D
=
AB . AP = AC . AD
AB . AB = AC . AD

4. A
a point is taken exterior to a circle, and
from the point a segment
is drawn tangent to the circle
and another segment (a secant)
is drawn which cuts the circle
in two distinct points, then
the square of the length
of the tangent is equal to the product
of the distance along the secant from
the external point
to the nearer point of intersection
with the circle and the distance
along the secant to the farther point
of intersection with the circle.
The proof 22 of this phytagorean
theorem uses power of point
theorem
C
B
DD

5. C
B
D
b
AB = c = AD + BD
BC = a
AC = b
A
Proof #22
Adding:
We Find Phytagorean Theorem: