A tangent is drawn to a circle at point $A$. A chord $AB$ is drawn such that it is parallel to another chord $BC$ (where $C$ is on the circumference). If $\angle ABC = 55^\circ$, find the size of $\angle BAC$.

A cyclic quadrilateral ${ABCD}$ is inscribed in a circle. If the side ${AD}$ is extended to a point ${E}$ outside the circle, which of the following statements is always true regarding the exterior angle $\mathrm{\angle }$?

The specific point where a tangent line meets the circumference of a circle without crossing into the interior is formally known as the:

A chord divides a circle into two distinct regions. What is the name specifically given to the region bounded by the chord and the major arc?

Fill in the blank: According to the central angle theorem, the angle subtended by an arc at the center is exactly ______ the angle subtended by the same arc at any point on the remaining part of the circumference.