Download Math 90 Unit 8 – Circle Geometry

Math 90 Unit 8 – Circle Geometry (Sections 8.1 – 8.3)
8.1 – Properties of Tangents to a Circle
Investigate: Page 384
A line that intersects a circle at only one point is a tangent to the
circle.
The point where the tangent intersects the circle is the point of
tangency.
For example: Line AB is a tangent to the circle with center O.
Point P is the point of tangency.
Tangent-Radius Property: A tangent to a circle is
perpendicular to the radius at the point of tangency. That
means that in the above circle, where the radius OP meets
the tangent AB, right angles are formed.
Assignment: Page 388 – 390, # 1 – 9, 12
Reflect in Journal
8.2 Properties of Chords in a Circle
Investigate: p. 392 - 393
A line segment that joins two points on a circle is chord. A
diameter of a circle is a chord that passes through the
center of the circle.
A perpendicular bisector intersects a line segment at a
90° angle and divides the line segment into two equal parts.
Perpendicular to Chord – Property 1: The perpendicular
line from the center of a circle to a chord bisects the
chord (divides the chord into two equal parts).
Perpendicular to Chord – Property 2: The perpendicular
bisector of a chord in a circle passes through the center
of circle.
Perpendicular to Chord – Property 3: A line that joins
the center of the circle and the midpoint of a chord is
perpendicular to the chord.
Assignment: Pages 397 – 399, # 1 – 7, 10, 18
Reflect in Journal
8.3 Properties of Angles in a Circle
Investigate: pg. 404 - 405
A section of the circumference of a circle is an arc.
The shorter arc AB is the minor arc (less than a semi-circle).
The longer arc AB is the major arc (greater than a semi-circle).
The angle formed by joining the endpoints of an arc to center of the circle
is a central angle. The angle formed by joining the endpoints of an arc to a
point on the circle is an inscribed angle. The inscribed and central angles in
the circle below are subtended by minor arc AB.
Central Angle and Inscribed Angle Property
In a circle, the measure of a central angle subtended by an
arc is twice the measure of an inscribed angle subtended
by the same arc.
Inscribed Angles Property
In a circle, all inscribed angles by the same arc are
congruent.
Angles in a Semicircle Property
All inscribed angles subtended by a semicircle are right
angles.
Assignment: Pages 410 – 412, # 3- 6, 8, Reflect in Journal
Do Circles Unit Review p. 418 – 419
Circles Hand-in Assignment