When segments intersect inside a circle, what is the relationship between the angle of intersection and the intercepted arcs?

Mathematics

2 answers:

rewona [7]3 years ago

8 0

They are supplementary angles because they both would have to add up to 180

Lelu [443]3 years ago

4 0

Answer:

Angle of intersection is one half of the sum of measurements of intercepted arcs.

Step-by-step explanation:

An inscribed angle is the angle formed by the intersection of two chords having a common endpoint in a circle.

Also, by the angles of Intersecting Chords Theorem,

When two chords intersect inside a circle, then the measure of the angle formed is one half of sum of the measure of the arcs intercepted by the angle and its vertical angle.

Which is the relationship between the angle of intersection and the intercepted arcs.

You might be interested in

Help needed on this composition math problem

Marrrta [24]

Given that f(x) = x/(x - 3) and g(x) = 1/x and the application of function operators, f ° g (x) = 1/(1 - 3 · x) and the domain of the resulting function is any real number except x = 1/3.

<h3>How to analyze a composed function</h3>

Let be f and g functions. Composition is a binary function operation where the variable of the former function (f) is substituted by the latter function (g). If we know that f(x) = x/(x - 3) and g(x) = 1/x, then the composed function is:

$f\,\circ\,g \,(x) = \frac{\frac{1}{x} }{\frac{1}{x}-3}$

$f\,\circ\,g\,(x) = \frac{\frac{1}{x} }{\frac{1-3\cdot x}{x} }$

$f\,\circ\,g\,(x) = \frac{1}{1-3\cdot x}$

The domain of the function is the set of x-values such that f ° g (x) exists. In the case of rational functions of the form p(x)/q(x), the domain is the set of x-values such that q(x) ≠ 0. Thus, the domain of f ° g (x) is $\mathbb{R} - \{\frac{1}{3} \}$ .