11.05 Angles from intersecting chords, secants, and tangents
Interactive practice questions
Consider circle $O$O with chord $\overline{AB}$AB and $\overleftrightarrow{BC}$›‹BCthat is tangent to $O$O at point $B$B.
If the measure of angle formed by $\overline{AB}$AB and $\overleftrightarrow{BC}$›‹BC is $\theta^\circ$θ°, what do we know about the measure of the intercepted arc?
The measure of the intercepted arc is half the difference between the $\overline{AB}$AB and $\overline{BC}$BC.
The measure of the intercepted arc is $\frac{\theta^\circ}{2}$θ°2.
The measure of the intercepted arc is $2\theta^\circ$2θ°.
The measure of the intercepted arc is unknown.
Consider circle $O$O with secant lines $\overleftrightarrow{AB}$›‹AB and $\overleftrightarrow{CD}$›‹CD intersecting at $E$E, a point inside the circle.
Consider the following circle centered at $O$O with tangents $\overline{AB}$AB and $\overline{AC}$AC that intersect the circle at points $B$B and $C$C respectively.
In the diagram below, the line $ST$ST is tangent to circle $\bigodot O$⊙O at the point$T$T.