ABC-AB-a-BC-b-AC-c-and-C-90-r-

Question Number 84304 by Wepa last updated on 11/Mar/20

Δ ABC AB = a BC = b AC = c

and ∠ C = 90 °

r = ?

Commented by mr W last updated on 11/Mar/20

r = \frac{a b}{a + b + c}

Answered by $@ty@m123 last updated on 11/Mar/20

G e n e r a l f o r m u l a :

r = \frac{△}{s}, △ = \frac{1}{2} a b \sin C

H e r e C = 90^{o}

∴ r = \frac{a b \sin 90^{o}}{2 \times \frac{a + b + c}{2}}

\Rightarrow r = \frac{a b}{a + b + c}