Property 15
\(A(ABC)=\samefrac12b\cdot c\cdot\sin\widehat A\)
\(A(ABC)=\samefrac12a\cdot c\cdot\sin\widehat B\)
\(A(ABC)=\samefrac12a\cdot b\cdot\sin\widehat C\)
Sinus Theorem
Side lenghts of ABC triangle are a, b, c
Radius of the circumscribed circle is R
\(\samefrac a{\sin\widehat A}=\samefrac b{\sin\widehat B}=\samefrac c{\sin\widehat C}=2R\)
\(\blacksquare\quad A(ABC)=\samefrac{a\cdot b\cdot c}{4R}\)
Area
\(a+b+c=2u\)
\(A(ABC)=u\cdot r\)
\(\blacksquare\quad a+b+c=2u\)
\(A(ABC)=\sqrt{u(u-a)(u-b)(u-c)}\)
1.
\(\Rightarrow A(ABC)=?\)
2.
\(\Rightarrow A(ABC)=?\)
3.
\(\Rightarrow x=?\)
4.
\(\Rightarrow \cos\alpha=?\)
5.
O center
\(\Rightarrow R=?\)
6.
O center
\(\Rightarrow x=?\)
7.
\(S_1=S_2\)
\(\Rightarrow x=?\)
8.
\(\Rightarrow r=?\)