Math, asked by sktskt3730, 10 months ago

P is a circumcenter of acute angle triangle ABC with circumradius R.midpoint of BC is D show that perimeter of triangle ABC is 2R( Sin A + sin b + sin c)

Answers

Answered by MaheswariS
0

\textbf{Concept used:}

\textsf{Sine formula:}

\textsf{In triangle ABC,}

\mathsf{\displaystyle\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}=2R}

\textsf{where R- circumradius}

\text{From sine fromula, we have}

a=2R\;sinA

b=2R\;sinB

c=2R\;sinC

\text{Now, Perimeter of $\triangle$ABC}

=\text{sum of all lengths of sides of $\triangle$ABC}

=a+b+c

=2R\;sinA+2R\;sinB+2R\;sinC

=2R(sinA+sinB+sinC)

\therefore\textbf{The perimeter of $\triangle$ABC is 2R(sinA+sinB+sinC)}

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