Question

please answer this question​

Answer 1

Answer:

your proof is as follows

pls mark it as brainliest

Step-by-step explanation:

$to \: prove : \\ A(△ABC)= \frac{1}{2} (AB+BC+AC) \times r \\ \\ so \: here \: since \\ adjoining \: circle \: is \: inscribed \: \\ in \: △ABC \\ it \: is \: its \: incircle \\ \\ so \: then \\ PM = inradius = r \\ \\ so \: we \: know \: that \\ inradius = \frac{2.area \: of \: circumsctibed \: triangle}{its \: perimeter} \\ \\ now \\ \: perimeter \: of \: △ABC = AB+BC+AC \\ \\ thus \: then \\ r .perimeter \: of \: △ABC = 2.A(△ABC) \\ \\ A(△ABC) = \frac{r.AB+BC+AC}{2} \\ \\ A(△ABC) = \frac{1}{2} \times (AB+BC+AC ) \times r \\ \\ hence \: proved$