1. Advanced Geometry Lesson 3 Circles
Tangents and Secants

2. Tangent If a line is tangent to a circle, then it is perpendicular
to the radius drawn to the point of tangency.

3. Example:
is tangent to
A at point C. Find x.

4. Example:
Determine whether
is tangent to
F. Justify your reasoning.

5. If two segments from the same exterior point are
tangent to a circle, then they are congruent.

6. Example:
Find x and y.

7. Example:
Triangle HJK is circumscribed about G.
Find the perimeter of
HJK if
NK = JL + 29.

8. Triangle JKL is circumscribed about R. Find x and the perimeter of
Example:
Triangle JKL is circumscribed about R.
Find x and the perimeter of
JKL. 10

9. Secant

10. whether they are both secants,
Two segments,
whether they are both secants,
both tangents,
or one secant and one tangent,
can intersect in one of three places:
In the Circle
On the Circle
Outside the Circle

11. Intersections Inside a Circle
If two secants intersect in the interior of a circle,
then the measure of an angle formed is one-half
the sum of the measure of the arcs intercepted
by the angle and its vertical angle.

12. Example:
Find m
4 if
= 88 and
= 76.

13. Intersections On a Circle
If a secant 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.

14. Example:
Find m
RPS if
= 114 and
= 136.

15. Intersections Outside of 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 positive difference of the measures of the
intercepted arcs.

16. Example:
Find x.
Find x.