HONORS GEOMETRY Special Segments in a Circle

Do Now: Find all missing variables. For bottom left find all missing arcs and angles.

Homework Questions? Comments? Confusions? Concerns? ASK ASK ASK ASK ASK!

Chord Segments When two chords intersect inside a circle, each chord is divided into two segments, called chord segments. EX: A and B are chord segments C and D are chord segments.

Segments of Chords Theorem If two chords intersect in a circle, then the products of the lengths of the chord segments are equal. ab=cd

Example One: Find x

Example Two: Find x

Example Three: Find x.

You Try! Find x

Example Four: An arch over an apartment entrance is 3 feet high and 9 feet wide. Find the radius of the circle containing the arc of the arch.

You Try! Scientists unearthed part of a circular wall. They made the measurements shown in the figure. Based on the information in the figure, what was the radius of the circle?

Sphere Equations:

Example Five: Find the surface area and volume of the sphere below

You Try! Find the surface area and volume of the sphere below

Example Six: If the area of a vertical cross section of a sphere is 94 mm squared, what is the surface area of the sphere?

You Try!

Example Seven: Ren inflates a spherical balloon to a circumference of about 14 inches. He then adds more air to the balloon until the circumference is about 18 inches. What volume of air was added to the balloon?

You Try! A puffer fish is able to “puff up” when threatened by gulping water and inflating its body. The puffer fish below is approximately a sphere with diameter of 5 inches. Its surface area when inflated is about 1.5 times its normal surface area. What is the surface area of the fish when it is NOT puffed up?

Practice Problems Try some on your own/in your table groups. As always don’t hesitate to ask me questions if you are confused OR talk to your tablemates! They are your greatest resource!

Exit Ticket: Find the surface area and volume of the sphere below. Also solve for x.