The points (0,9),(12,0) and (0,0) create a right triangle. Find

Finley Mckinney

Finley Mckinney

Answered question

2022-06-21

The points (0,9),(12,0) and (0,0) create a right triangle. Find the equation of the angle bisectors for each of the three angles on the triangle.

I am unsure of how to find the equations. Any help will be greatly appreciated!

Answer & Explanation

arhaitategr

arhaitategr

Beginner2022-06-22Added 13 answers

A possible approach is to find the location of the incenter through
I = a A + b B + c C a + b + c = ( 3 , 3 )
then the equations of the lines A I , B I , C I are pretty straightforward.
Damon Stokes

Damon Stokes

Beginner2022-06-23Added 6 answers

Here is an approach for the bisector at (0,9).

The angle θ at (0,9) has cos θ = 9 15 = 3 5 , so the tangent of the half-angle is
tan θ 2 = 1 cos θ 1 + cos θ = 1 2 .
This means that the bisector from (0,9) intersects the x-axis at ( 9 2 , 0 ). So just find the equation of the line containing (0,9) and ( 9 2 , 0 ).

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