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GEOMETRY: Chapter 10
10.4: Other Relationships in Circles
Theorem 10.12
If a tangent and a chord intersect at a point on a
circle, then the measure of each angle formed
is one half the measure of its intercepted arc.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 680.
Ex.1:
Line m is tangent to the circle. Find x or y.
Answer: a. 114; b. 236
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681.
Intersecting Lines and Circles
If two lines intersect a circle, there are three
places where the lines can intersect.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681.
Angles Inside the Circle Theorem
If two chords intersect inside a circle, then the
measure of each angle is one half the sum of
the measures of the arcs intercepted by the
angle and its vertical angle.
Theorem 10.13:
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681.
Angles Outside the Circle Theorem
If a tangent and a secant, two tangents, or two
secants intersect outside a circle, then the
measure of the angle formed is one half the
difference of the measures of the intercepted
arcs.
Theorem 10.14
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681.
Ex. 2:
Find the value of x.
Answer: 76
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681.
Ex. 3:
Find the value of x.
Answer: 18
Images taken from: Geometry. McDougal Littell: Boston, 2007. P.682.
Ex. 4:
The Space Shuttle typically orbits at a height of 600
kilometers. Suppose an astronaut takes a picture
from point S. What is the measure of arc RQ?
Answer: 48o
Images taken from: Geometry. McDougal Littell: Boston, 2007. P.682.
10.4, p. 624, #5-28 all