Question

a secant and a tangent meet at a 90° angle outside the circle. what must be the difference between the measures of the intercepted arcs? 45°, 90°, 180°, 270°

Explanation:

Step1: Recall the angle - outside - the - circle formula

The measure of the angle formed by a secant and a tangent outside a circle is given by $\frac{1}{2}(m\overset{\frown}{major}-m\overset{\frown}{minor})$.

Step2: Set up the equation

We know the angle between the secant and the tangent is 90°. Let the measure of the major arc be $x$ and the measure of the minor arc be $y$. So, $90^{\circ}=\frac{1}{2}(x - y)$.

Step3: Solve for $x - y$

Multiply both sides of the equation $90^{\circ}=\frac{1}{2}(x - y)$ by 2. We get $x - y=180^{\circ}$. So the difference between the measures of the intercepted arcs must be 180°.

Answer:

180°