Question

which statements are true regarding the diagram for circle p and the angles created? check all that apply.$angle dec$ is a circumscribed angle.$angle bca$ is an inscribed angle.$angle cba$ is a central angle.$angle apb$ is a central angle.$overline{pb} cong overline{pa}$$overline{ec} cong overline{cb}$

Explanation:

1. A circumscribed angle is formed by two tangent lines to a circle. $\angle DEC$ is formed by tangents $ED$ and $EC$ to circle $P$, so it is a circumscribed angle.
2. An inscribed angle has its vertex on the circle and sides as chords. $\angle BCA$ has vertex $C$ on the circle, with sides $CB$ and $CA$ as chords, so it is an inscribed angle.
3. A central angle has its vertex at the circle's center. $\angle CBA$ has vertex $B$ on the circle, not the center $P$, so it is not a central angle.
4. $\angle APB$ has vertex at center $P$, with sides as radii $PB$ and $PA$, so it is a central angle.
5. $\overline{PB}$ and $\overline{PA}$ are both radii of circle $P$, and all radii of a circle are congruent.
6. $\overline{EC}$ is a tangent segment, $\overline{CB}$ is a chord; there is no given or inherent property that makes these segments congruent.

Answer:

$\boldsymbol{\angle DEC}$ is a circumscribed angle.
$\boldsymbol{\angle BCA}$ is an inscribed angle.
$\boldsymbol{\angle APB}$ is a central angle.
$\boldsymbol{\overline{PB} \cong \overline{PA}}$