A theorem in geometry states that the measure of an inscribed angle is half the measure of its intercepted arc. 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?
A. (b/c-a) (b/c+a) = -1
B. (b/a-c) (b/a+c) = -1
C. (b/-c) (b/c) = -1
D. (b/a-c) (b/a+c) = 1

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

ahirohit963 ahirohit963 · Answer 2 · 2021-11-20T09:29:45+01:00

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).

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https://brainly.com/question/17517783