Respuesta :
Answer:
B. (b/a-c) (b/a+c) = -1
Step-by-step explanation:
In the figure, angle C intercepts arc AB and line AB is the diameter of the circle. Which equation is a step in showing that the measure of angle C=90 degrees?
Slope of AC = [tex]\frac{b-0}{a-(-c)} = \frac{b}{a+c}[/tex]
Slope of CB =
[tex]\frac{0-b}{c - a} =\frac{b}{a-c}[/tex]
If LC = 90°
Then,
Slope of AC × Slope of BC = -1
[tex](\frac{b}{a-c} )(\frac{b}{a+c} )=-1[/tex]
Therefore, the correct answer is
[tex](\frac{b}{a-c} )(\frac{b}{a+c} )=-1[/tex]
Option B
The equation that is a step in showing that the measure of angle C = 90 degrees is given by [tex]\rm\left( \dfrac{b}{a-c}\right)\left(\dfrac{b}{a+c}\right) =-1[/tex] and this can be determined by using the properties of geometry.
Given :
- A theorem in geometry states that the measure of an inscribed angle is half the measure of its intercepted arc.
- Angle C intercepts arc AB and line AB is the diameter of the circle.
First, determine the slope of AC:
[tex]\rm m_{AC}= \dfrac{b-0}{a-(-c)}[/tex]
[tex]\rm m_{AC}= \dfrac{b}{a+c}[/tex]
Now, evaluate the slope of CB:
[tex]\rm m_{CB}=\dfrac{0-b}{c-a}[/tex]
[tex]\rm m_{CB}=\dfrac{-b}{c-a}[/tex]
According to the given data, the measure of angle C = 90 degrees. That implies:
[tex]\rm m_{AC}\times m_{CB} = -1[/tex]
Now, put the values of both the slopes in the above equation.
[tex]\rm \dfrac{b}{a+c}\times \dfrac{-b}{c-a} = -1[/tex]
[tex]\rm\left( \dfrac{b}{a-c}\right)\left(\dfrac{b}{a+c}\right) =-1[/tex]
Therefore, the correct option is B).
For more information, refer to the link given below:
https://brainly.com/question/17517783
