Chapter 9 Calendar
9-1: Basic Terms
9-2: Tangents
CM3IQFWYL
A polygon is inscribed in a circle when each of its vertices lies on
the circle. Draw some pictures: in a circle, is it possible to
inscribe…
1) a parallelogram that is not a rectangle?
2) a non-isosceles trapezoid?
3) a non-regular pentagon?
9-1 Objectives
• Define a circle, sphere, and terms related to
them
• Recognize circumscribed/inscribed polygons
A
A
is:
is:
Parts of a Circle
·
Draw two tangent segments to a circle from the same
point outside the circle. Make a conjecture about the
tangent segments.
Draw a circle with center 𝑂 and radius 𝑂𝐴. Draw 𝐴𝑇
perpendicular to 𝑂𝐴. What kind of segment must 𝐴𝑇
be?
More
have the same
____________.
are coplanar and have the
same _____________.
A polygon is
A polygon is
in a circle when…
about a circle when…
Points 𝐴 and 𝐵 lie on ⨀𝑂, which has a radius of
10 𝑚. Find the length of 𝐴𝐵 if m∠𝐴𝑂𝐵 = 80°.
9-2 Objectives
State, prove, and apply
tangents and radii of circles.
that relate to
Using Triangles in Circles
Draw two congruent circles with radii 12, each
passing through the center of the other. Find the
length of their common chord.
If a line is tangent to a circle,
then it is perpendicular to the radius at the
point of tangency.
A line that is tangent to two coplanar circles is
called a
.
If it intersects the segment joining their centers,
it is an
:
If not, it’s an
:
Example
Circles O and P have radii 6 and 4 respectively. Find the length
of their common external tangent segment.
Circles that intersect at one point are called
Tangent segments to a circle from an external
point are congruent.
Example
𝐴𝐵 and 𝐶𝐷 are common internal tangents. If
𝐴𝑃 = 8 and 𝑃𝐵 = 6, find 𝐶𝐷.
Example
An equilateral triangle of perimeter 18 𝑐𝑚 is
circumscribed about a circle. Find the
circumference of the circle.
p. 330: #1-17 odd, 18
Draw a picture for all
• If you have a compass or some tool for
drawing nice circles, use it!
p. 335: #1-11 odd, 17, 18