Principle Of Mathematical Induction

Question
CBSEENMA11014350

Prove that in any triangle ABC

            space space space space space space straight r space equals space straight capital delta over straight s

Solution

Let I be incentre of the triangle ABC
 
                  
Join ID, IE and IF which are perpendicular to BC, CA and AB respectively
                    ID = IE = IF = r (In radius)
Now, area of the triangle ABC = straight capital delta
                                           = Area of triangle IBC + Area of triangle ICA + Area of triangle IAB
                                            equals 1 half ID. space BC space plus space 1 half IE. space CA space plus space 1 half IF. space AB space equals space 1 half straight r. straight a space plus space 1 half straight r. straight b space plus space 1 half straight r. straight c
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#6 {main}</pre>
or                          straight r equals straight capital delta over straight s

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