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Master Chord Properties: Key Concepts in Circle Geometry

TX.G.10.A

Surface area of 3-dimensional shapes

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

TX.G.10.B

auto-gen

Upper and lower bound

Upper and Lower Bound

TX.G.11.B

Areas and sectors of circles

TX.G.11.C

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

TX.G.11.D

Introduction to volume

Calculate the Volume

TX.G.12.A

Angles in a circle

Chord properties

Tangent properties

Circles and circumference

Circle properties

Central angles and proofs

Inscribed angles and proofs

Central and inscribed angles in circles

TX.G.12.B

Arcs of a circle

Circle chord, tangent, and inscribed angles proofs

TX.G.12.D

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

TX.G.12.E

Conics - Circle

TX.G.13.A

Permutations

Combinations

Problems involving both permutations and combinations

TX.G.13.B

Probability

TX.G.13.C

Probability of independent events

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

TX.G.13.D

Conditional probability

Probability with Venn diagrams

TX.G.13.E

Determining probabilities using tree diagrams and tables

Probability involving permutations and combinations

TX.G.2.A

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

TX.G.2.B

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Parallel and perpendicular lines in linear functions

TX.G.2.C

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

TX.G.3.A

Rotational symmetry and transformations

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

TX.G.3.B

Combining transformations of functions

Enlargements and reductions with scale factors

TX.G.3.C

Scale diagrams

TX.G.3.D

Line symmetry

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

TX.G.4.A

Inductive reasoning

Deductive reasoning

TX.G.4.B

Conditionals

Inverses, converses, and contrapositives

Biconditionals

TX.G.4.D

Algebraic proofs

TX.G.5.A

Congruence and congruent triangles

Pairs of lines and angles

Parallel lines and transversals

Perpendicular line proofs

TX.G.5.D

Classifying triangles

TX.G.6.A

Isosceles and equilateral triangles

Parallel line proofs

TX.G.6.B

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

TX.G.6.D

Combination of SohCahToa questions

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

TX.G.6.E

Classifying quadrilaterals

Classifying Quadrilaterals

Word Problem: Classifying Quadrilaterals

TX.G.7.A

Similar triangles

Similar polygons

TX.G.8.B

Estimating square roots

TX.G.9.A

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

TX.G.9.B

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Circles

Coordinate and transformational geometry

Logical argument and constructions

Proof and congruence

Two-dimensional and three-dimensional figures

math

Intro

- Hi, welcome to this question right here. So, we know that A to C is four centimeters. So, let me just put that down right here for you. So, there's four centimeters from here to here, okay? And B to D is from here to here, it's 15 centimeters in total. But instead of me doing the 15, I'm going to divide it into two first, okay? Because. . . So, 15 divided by two is 7.5 but, because this is a bisector so, these two sides right here, the two segments here and here, they're both equal. So, the total is 15, if you divide it by two you get 7.5 from here and it's 7.5 here as well, okay? So, we're still good? 
Take a look, they're looking for the diameter of the circle but, we can actually draw our own radius. See, from here to here, A to B, the reason why I actually draw a line right here is because I want to form a right triangle, okay? 
So, there's our right triangle right here. I know this side's a four, this is my right angle 90 degrees. And I know this side's 7.5. This is actually known as your C, which is the radius or the hypotenuse, the C or the hypotenuse, right? 
So, why are we looking for this? Because this is your radius, okay? So, why are we looking for the radius? Well, if you can figure out your radius times by two, what do you have? Diameter, right? So, that's why we need to find the radius first. So to find the C, remember you have the Pythagoras theorem. So, we've got four square plus 7.5 square and just find the C. All you have to do is square root the whole thing, once you figure this out. So, grab your calculator and go four square, plus 7.5 square and don't forget to square root the whole thing. I have 8.5. Now, remember, this is your radius, okay? 
The radius is 8.5, what about diameter? 
Well, why don't we just times by two. So, the diameter for this question is just 8.5 times by two, the answer turns out to be just 17 centimeter. And that is the answer for this question. Thanks for watching.

In a circle, when a line passes through the center of the circle and is perpendicular to a chord, the line will bisect the chord. In other words, the perpendicular bisector of a chord always passes through the center of the circle. 