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 $\mathrm{\angle }$?

Sector A has a radius of $5 \text{ units}$ and a central angle of $2 \text{ radians}$. Sector B has a radius of $10 \text{ units}$ and a central angle of $1 \text{ radian}$. Which of the following statements is true regarding their areas?

In the derivation of the distance formula $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$, what does the expression represent?

In the context of the 'shape recipe' analogy, what remains constant for all right triangles with an acute angle of $25^\circ$, regardless of the triangle's physical size?