This is a summary of chapter 10, enjoy!
They will be short and sweet...
Click this
link for a breif lesson on being fooled.
10.1
In this chapter aka. "The Circle" were we learned about circles (which the title clearly tells you). A circle is the set of all points in a plane that are a givin distance from a given point on the plane. The given point is the
center of the circle, and the given distance is the
radius. We also learned what chords and diameters are.
The theoroms we learned were;
74-If a radius is perpindicular to a chord, then it bisects the chord.
75-If a radius of a circle bisects a chord that isnt a diameter, it is
perpindicular to that chord.
76-The perpendicular bisector of a chord passes through the center of the circle.
"Congruent Chords"
10.2
We learned 2 main theorems in this chapter...
77-If two chords of a circle are equadistant form the center, then they are
congruent.
78-If two chords of a circle are congruent, then they are equadistant from the
center of the circle.
10.3 is about "Arcs of circles"
An ark was a temporary boat used for river transport in eastern North America before canals and railroads made them obsolete. Arks were built primarily to carry cargo downriver on the spring freshet to carry lumber or logs and agricultural produce to a port city downriver...
But an arc consists of two points on a circle and points on the circle needed to connect the points by a single path.
There are two types or arcs;
Next is 10.4 "Secants and tangents"
A
Secant is a line that intersects a circle at exactly two points(contains a chord)
A
tangent is a linethat intersects a circle at exactly one point. This point is called the point of tangency or point of contact.
Another important thing is when you have your common external tangent, you want to add both circles radius and the difference for the height, then use the pythagorean theorem to solve the exterior tangent length.
Later we learn Theorom 85; If two tangent segments are drawn to a circle from an external ppoint,then those segments are congruent.
On to 10.5
Heres the big picture... click it to make it bigger!
Inscribed
Chord-Chord
Tangent-Chord
Secant-Secant angle
Secant-tangent angle
tangent-tangent angle
Fun right? good thing we still have more chapters to do...
Chapter 10.6: More Angle- Arc Theorems
89-If two inscribed or tangent-chord angles intercept the same arc, then they
are congruent.
90- If two inscribed or tangent- chord angles intercept congruent arcs, then
they are congruent.
91-An angle inscribed in a semicircle is a right angle.
92-The sum of the measures of a tangent-tangent angle and its minor arc is 180*
(degrees)
No pictures on this one, sorry ive been at this for over 2 hours and i want sleep...
10.8 (No 10.7 we didnt do it)
"Power Theorems"
Theorem 1-If two chords of a circle intersect inside the circle, then the product of the measures of the segments of one chord are equal to the product of the measures of the other chord.
Theorem 2- (during only 2 secant segments)If two secant segments are drawn from an external point to a circle, then the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part.
Theorem 3- (one tangent line and one secant line in the circle)If a tangent and a secant segment are drawn from an external point to a circle, then the square of the measure of the tangent segment is equal to the product of the measures of the entire secant segment and its external part.
That wraps up my chapter 10 review and I want to say thanks for the Great Honors Geometry class,
you booklickers...
-Tyler Rogers-
Dog on a Frog on a Blog.
The first theorem is.... -If two chords of a circle intersect inside the circle, then the product of the measures of the segments of one chord are equal to the product of the measures of the other chord.
