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Triangle


Elements of the triangle ::

about ::

Median (geometry) - Wikipedia

The interior angle bisectors of a triangle

Circumscribed circle - Wikipedia

Law of sines - Wikipedia

Law of cosines - Wikipedia

Law of cotangents - Wikipedia

Law of tangents - Wikipedia

Mollweide's formula - Wikipedia

Heron's formula - Wikipedia

Orthocenter

...

def ::

{a2=b2+c22bc·Cos αb2=c2+a22ca·Cos ßc2=a2+b22ab·Cos γ

2·p=P=a+b+c

abc4R=pr=S=p(pa)(pb)(pc)

2R2 Sin α Sin ß Sin γ=S=p2 Tan α2 Tan ß2 Tan γ2


{ha=2a·Shb=2b·Shc=2c·S

1r=1ha+1hb+1hc

r2=(pa)(pb)(pc)p

2·R=aSin α=bSin ß=aSin γ

R=abc(a+bc)(b+ca)(c+ab)(a+b+c)

S={a·ha2b·hb2c·hc2={bc·Sin α2ca·Sin ß2ab·Sin γ2={a2 Sin ß Sin γ2 Sin αb2 Sin γ Sin α2 Sin ßc2 Sin α Sin ß2 Sin γ



some x-ref formulas to verify the above figure and formulas ::

Some basics ::

The intersection of two lines ::

{y=a0·x+b0y=a1·x+b1  [Δs=s1s0] 

from: y=ax+b0=x·Δa+Δbthus:x= ΔbΔa= b1b0a1a0from: ya=x+bay·Δ1a=0+Δbathus:y=ΔbaΔ1a=b1a1b0a01a11a0=a0b1a1b0a0a1

The intersection of an arbitrary line and the perpendicular line crossing it drawn through an arbitrary point ::

! note : the slope for the perpendicular line in the below tutor is
my notation : a= 1a (about : Parallel and perpendicular symbol from Mathematica to $\LaTeX$ - Mathematica Stack Exchange)
the notation in the video tutor : m= 1m



The intersection of two Circles ::

... write out general , analytical solution for the system :

{(xa0)2+(yb0)2=R0(xa1)2+(yb1)2=R1

etc. ...


 [Eop]

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