Geometry SAT Problem: Area of Smaller Circle with Bisected Angle | Homework Help

In summary, the problem involves a right circular cone with 2 circles centered at point A on its base. The height of the cone is AB, the measure of angle ABC is 60°, and the length of BC is y. The question asks for the area of the smaller circle in terms of y. The picture provided shows that BD bisects angle ABC, not the line segment AC. This may lead to confusion in finding the correct answer.
  • #1
athena810
22
0

Homework Statement


A right circular cone is drawn above, with 2 circles centered at A on its base as shown. AB is the height of the cone, the measure of <ABC is 60° and BC has a length of y. If BD bisects <ABC, which one of the following gives the area of the smaller circle in terms of y?

http://imgur.com/JgrevjM

Homework Equations



none

The Attempt at a Solution


Included in the picture

Could you explain what I did wrong, and how to get the correct answer? Thanks
 
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  • #2
BD doesn't bisect AC.
 
  • #3
Doesn't bisecting cause the bisecting thing to bisect the line segment from where the angles end?
 
  • #4
It bisects the angle ABC, it does not cut the line AC in half (which seems to be what you are using)
 

1. What is the formula for finding the area of a circle?

The formula for finding the area of a circle is A = πr², where A is the area and r is the radius of the circle.

2. How do you find the area of a smaller circle with a bisected angle?

In order to find the area of a smaller circle with a bisected angle, you will need to use the formula A = πr²/2, where A is the area and r is the radius of the circle. This is because the bisected angle reduces the area of the circle by half.

3. Can you explain how to solve a geometry SAT problem involving the area of a smaller circle with a bisected angle?

Sure! To solve this type of problem, you will first need to identify the given information, such as the radius of the larger circle and the measurement of the bisected angle. Then, use the formula A = πr²/2 to find the area of the smaller circle. Make sure to pay attention to units of measurement and round your answer to the appropriate number of significant figures.

4. Is there a specific method for solving geometry SAT problems?

Yes, there are several strategies for solving geometry SAT problems. These include drawing a diagram, identifying given information and relationships, and using formulas and equations to solve for unknown values. It is also important to carefully read and understand the problem before attempting to solve it.

5. Are there any common mistakes to avoid when solving geometry SAT problems?

One common mistake to avoid is using the wrong formula or plugging in incorrect values. It is important to carefully read the problem and double check your work to ensure that you are using the correct formula and values. It is also helpful to label your diagram and clearly show your steps in your solution to avoid any errors.

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