ABC-is-a-triangle-with-points-A-5-5-B-5-10-C-15-5-the-cartesian-equtions-of-AB-AC-and-BC-are-respectively-x-5-y-5-x-y-5-1-Please-help-me-to-determinate-the-cartesian-equations-of-t

Question Number 78453 by mathocean1 last updated on 17/Jan/20

ABC is a triangle with points

A (- 5; - 5) B (- 5; 10) C (15; - 5) .

the cartesian equtions of (AB); (AC)

and (BC) are respectively

x = - 5

y = - 5

x + y = 5

1) Please help me to determinate

the cartesian equations of the

interior bisectors of \hat{A}; \hat{B}; \hat{C} .

2) Demonstrate that these bisectors

meet in some point H (25; 25)

3) Give a cartesian equation of

inscrited circle in ABC triangle .

Commented by mathocean1 last updated on 17/Jan/20

Hello Please sirs can you help me \dots

Commented by john santu last updated on 18/Jan/20

c a r t e s i a n e q u a t i o n o f i n t e r i o r b i s e c t o r

\hat{A} : s l o p e m = \tan \frac{π}{4} = 1

y = 1 (x + 5) + (- 5) \Rightarrow y = x

Commented by john santu last updated on 18/Jan/20

c a r t e s i a n e q u a t i o n o f

t h e i n t e r i o r b i s e c t o r o f \hat{B}

w i t h s l o p e = - \cot α = - 2 a n d

p a s s i n g t h r o u g t B (- 5, 10)

\Rightarrow y = - 2 (x + 5) + 10

y = - 2 x

Commented by john santu last updated on 18/Jan/20

c a r t e s i a n e q u a t i o n o f t h e

i n t e r i o r b i s e c t o r \hat{C}

w i t h s l o p e = - \tan β = - \frac{1}{3}

y = - \frac{1}{3} (x - 15) + (- 5)

y = - \frac{1}{3} x