a secant and a tangent meet at a 90° angle outside the circle. what must be the difference between the…

Answer:

C. $180^{\circ}$

Explanation:

Step1: Recall the formula

The measure of the angle formed by a secant - tangent pair outside a circle is given by $\theta=\frac{1}{2}(m\overset{\frown}{AB}-m\overset{\frown}{CD})$, where $\theta$ is the angle between the secant and the tangent, and $m\overset{\frown}{AB}$ and $m\overset{\frown}{CD}$ are the measures of the intercepted arcs.

Step2: Substitute the given angle

We are given that $\theta = 90^{\circ}$. Substituting $\theta = 90^{\circ}$ into the formula $90^{\circ}=\frac{1}{2}(m\overset{\frown}{AB}-m\overset{\frown}{CD})$.

Step3: Solve for the difference of the arcs

Multiply both sides of the equation by 2: $2\times90^{\circ}=m\overset{\frown}{AB}-m\overset{\frown}{CD}$. So, $m\overset{\frown}{AB}-m\overset{\frown}{CD}=180^{\circ}$.