Geometry
# Properties of Circles

$r,$ with $\angle ABC=15^\circ.$ If the length of arc $\widehat{AC}$ is equal to $10,$ what is the measure of $r?$

The above diagram shows a circle of radius**Note:** The above figure is not drawn to scale.

$O$ is the center of the circle. If $\angle BDC=26^\circ,$ what is $\angle BCA$ in degrees?

In the above diagram, point**Note:** The above figure is not drawn to scale.

$\widehat{BC}$ and $\widehat{CD}$ are equal. If $\angle BAC=20^\circ$ and $\angle ABD=40^\circ,$ and the measure of arc $\widehat{BC}$ is equal to $6,$ what is the measure of arc $\widehat{APB}?$

In the diagram above, the measures of the two arcs**Note:** The above figure is not drawn to scale.

$AB$ and $BC$ are tangent lines of a circle, with points $A$ and $C$ as their respective tangent points. If $\angle ADC=70^\circ,$ what is $\angle ABC$ in degrees?

In the diagram above, lines