a theorem in geometry states that the measure of an inscribed angle is half the measure of its intercepted…

a theorem in geometry states that the measure of an inscribed angle is half the measure of its intercepted arc. in the figure, ∠c intercepts arc ab and ab is the diameter of the circle. which equation is a step in showing that m∠c = 90°?

a theorem in geometry states that the measure of an inscribed angle is half the measure of its intercepted arc. in the figure, ∠c intercepts arc ab and ab is the diameter of the circle. which equation is a step in showing that m∠c = 90°?

Answer

Explanation:

Step1: Record los puntos dados

Tenemos $A(-c,0)$, $B(c,0)$ y $C(a,b)$.

Step2: Encontrar las pendientes de $AC$ y $BC$

La pendiente de la recta $AC$, $m_{AC}=\frac{b - 0}{a + c}=\frac{b}{a + c}$. La pendiente de la recta $BC$, $m_{BC}=\frac{b-0}{a - c}=\frac{b}{a - c}$.

Step3: Usar la propiedad de ángulos rectos

Si $\angle C = 90^{\circ}$, entonces las rectas $AC$ y $BC$ son perpendiculares. Para dos rectas perpendiculares, el producto de sus pendientes es $- 1$. Entonces $m_{AC}\times m_{BC}=-1$, es decir $\left(\frac{b}{a + c}\right)\left(\frac{b}{a - c}\right)=-1$.

Answer:

$\left(\frac{b}{a + c}\right)\left(\frac{b}{a - c}\right)=-1$