Transcript Inscribed Angle - Lockland Schools

Moving on with Circles…..
Going round and round again…
Feb. 24, 2014
Geometry—Mr. Morrison
7th period

What we already know…
 The radius of a circle is the distance from the center of the circle
to the outside edge.
 The diameter of a circle is longest distance across a circle. (The
diameter cuts through the center of the circle. This is what makes
it the longest distance.)
 Now take a look at this….
https://www.khanacademy.org/math/geometry/cc-geometrycircles/circles/v/language-and-notation-of-the-circle
Area and Circumference……

The circumference of a circle is the perimeter -- the distance around the
outer edge.

Circumference =
where r = the radius of the circle
and pi = 3.141592...

Area =
where r = the radius of the circle
and pi = 3.141592…

A quick video refresher…..

https://www.khanacademy.org/math/geometry/basicgeometry/circum_area_circles/v/circles--radius--diameter-andcircumference
Circles—the inner workings……
 A chord of a circle is a line segment that connects one point on the
edge of the circle with another point on the circle.
(The diameter is a chord -- it's just the longest chord!)
 An arc of a circle is a segment of the circumference of the circle.
 A quick video:
https://www.khanacademy.org/math/geometry/cc-geometrycircles/circles/v/length-of-an-arc-that-subtends-a-central-angle
Central Angle Measurements
 Central Angle:
A central angle is an angle formed by two intersecting radii such
that its vertex is at the center of the circle.
 Central Angle = Intercepted Arc
 <AOB is a central angle.
Its intercepted arc is the minor arc from A to B.
m<AOB = 80°
Inscribed Angle Measurement
 Inscribed Angle:
An inscribed angle is an angle with its vertex "on" the circle,
formed by two intersecting chords.
 Inscribed Angle =1/2 Intercepted Arc
 <ABC is an inscribed angle.
Its intercepted arc is the minor arc from A to C.
m<ABC = 50°

Special Situations for Inscribed Angles
 Special situations involving inscribed angles:
 An angle inscribed in a
semi-circle is a right angle.
 In a circle, inscribed circles that intercept the same arc are
congruent.
Special situations for inscribed angles
 A quadrilateral inscribed in a circle is called a cyclic
quadrilateral.
 The opposite angles in a cyclic quadrilateral are
supplementary.
Sectors
 A sector of a circle is a pie shaped portion of the area of the
circle. Technically, the piece of pie is between two segments
coming out of the center of the circle.
 Start the practice with worksheet…..