Pythagore: exercice\ avec\ utilisation\ du\ théorème.

Calculer\ LM.

\textcolor{red}{\underline{\textcolor{black}{On\ sait\ que}}}:

le\ triangle\ KLM\ est\ rectangle\ en\ K.

\textcolor{red}{\underline{\textcolor{black}{On\ utilise}}}:

le\ \textbf{\textit{théorème}}\ de\ Pythagore.

\textcolor{red}{\underline{\textcolor{black}{On\ en\ déduit\ que}}}:

KL²+KM²=LM².

\textbf {Exercice}

\textbf {Corrigé}

MathsEnClair.com

K

L

M

45

60

?

En\ utilisant\ les\ distances\ connues\ on\ obtient:

45²+60²=LM²\ 
\Leftrightarrow 2025+3600=LM²\ 
\Leftrightarrow 5625=LM²\ 
\Leftrightarrow LM=+\sqrt{5625}.

A\ l\text{'}aide\ de\ la\ calculatrice,on\ obtient:  \textbf{\textit{LM=75}}.

e = 1 (slider from 1 to 9, step 1)
L = (-104.68743643606959, -2.557451337617643)
K = Point(Circle[L, 45])
a = Segment(L, K)
b = OrthogonalLine(K, a)
c = Circle(K, 60)
M = Intersect(c, b, 1)
d = Segment(L, M)
e_1 = Segment(M, K)
α = Angle(L, K, M)
A = Midpoint(K, L)
B = Midpoint(K, M)
C = Midpoint(L, M)