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

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Homework Help Overview

The problem involves a right circular cone with two circles centered at a point on its base. The focus is on the geometry of the cone, specifically the relationship between the angle formed and the dimensions of the circles, particularly the area of the smaller circle in terms of a variable length.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are discussing the implications of angle bisectors in the context of the geometry presented. There are questions about the correctness of the original poster's assumptions regarding the properties of the angle bisector and its relationship to the line segments involved.

Discussion Status

The discussion is ongoing, with participants providing clarifications about the geometric properties involved. Some guidance has been offered regarding the nature of angle bisectors and their effects on line segments, but no consensus has been reached on the correct interpretation of the problem.

Contextual Notes

There appears to be confusion regarding the definitions and properties of angle bisectors in relation to the segments of the cone's geometry. The original poster has requested clarification on their approach and the assumptions made in their reasoning.

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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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BD doesn't bisect AC.
 
Doesn't bisecting cause the bisecting thing to bisect the line segment from where the angles end?
 
It bisects the angle ABC, it does not cut the line AC in half (which seems to be what you are using)
 

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