Talesov izrek: razlika med redakcijama

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'''Tálesov izrèk''' je [[izrek]] (imenovan v čast [[Tales]]u) v [[geometrija|geometriji]], ki pravi, da je obodni [[kot]] nad [[premer]]om [[krožnica|krožnice]] [[pravi kot|pravi]]; če imamo torej premer ''AC'' neke krožnice in od ''A'' in ''C'' različno [[točka|točko]] ''B'' na njenem obodu, je kot '''ACB''' pravi kot.
 
[[Slika:Image:Thales-proof.png|thumb|250px|Talesov izrek]]
[[Slika:Thaleskreis Kreistangente.jpg|thumb|250px|Konstrukcija tangente]]
== Dokaz: ==
 
Let O be the center of the circle. Since OA = OB = OC, OAB and OBC are
isosceles triangles, and by the equality of the base angles of an
isosceles triangle, OBC = OCB and BAO = ABO. Let γ = BAO and δ = OBC.
 
Since the sum of the angles of a triangle is equal to two right
angles, we have
 
:2γ + γ ′ = 180°
 
and
 
:2δ + δ ′ = 180°
 
We also know that
 
:γ ′ + δ ′ = 180°
 
Adding the first two equations and subtracting the third, we obtain
 
:2γ + γ ′ + 2δ + δ ′ − (γ ′ + δ ′) = 180°
 
which, after cancelling γ ′ and δ ′, implies that
 
:γ + δ = 90°
 
'''[[Q.E.D.]]'''
 
Dokaz: