1. Secants, Tangents, and Angle Measure

2. Intersections On or Inside a Circle that intersects a circle
A line
that intersects a circle
in exactly two points
is called a secant

3. Intersections On or Inside a Circle
If two secants or chords
intersect in the interior of a circle
then the measure of the angle formed
is one half the sum of the measure
of the arcs intercepted
by the angle and its vertical angle

4. Intersections On or Inside a Circle
is one half the sum of the measure
by the angle and its vertical angle
then the measure of the angle formed
intersect in the interior of a circle
If two secants or chords
of the arcs intercepted x 1 y

5. Intersections On or Inside a Circle45 65 1

6. Intersections On or Inside a Circle
If a secant (or chord) and a tangent
intersect at the point of tangency
Then the measure of each angle formed
is one half the measure of its intercepted arc.

7. Intersections On or Inside a Circle
of its intercepted arc
Then the measure of each angle formed
is one half the measure
If a secant (or chord) and a tangent
intersect at the point of tangency x y 1 2

8. Intersections On or Inside a Circle
200
160 1 2

9. Intersections Outside a Circle
If secants and tangents
intersect outside a circle
they form an angle
whose measure is related to the intercepted arcs

10. Intersections Outside a Circle
If two secants, a secant and a tangent, or two tangents
intersect in the exterior of a circle
then the measure of the angle formed
is one half the difference
of the measures of the intercepted arcs

11. Intersections Outside a Circle
Two secants 1 y x

12. Intersections Outside a Circle
A secant and a tangent x y 1

13. Intersections Outside a Circle
Two tangents x y 1