Help with Geometry Proof: Find CD in terms of AD and BD

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Homework Help Overview

The problem involves a geometric proof related to a circle with diameter AB and a point C on the circle. The goal is to find the length CD in terms of lengths AD and BD, utilizing properties of triangles formed within the circle.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the properties of triangle ABC and its relationship to the circle, including the nature of angles and sides. There are suggestions to consider the center of the circle and the implications of connecting points A, B, and C.

Discussion Status

The discussion is ongoing, with participants exploring various properties of the triangle and the circle. Some have proposed methods involving the center of the circle, while others are seeking clarification on specific angles and triangle types.

Contextual Notes

Participants are working within the constraints of a geometry proof and are focused on deriving relationships without providing explicit solutions. There is an emphasis on understanding the properties of the triangle and the circle.

Maluka8
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I need help in how to do this proof.


A circle is given with diameter AB. pick any point C on the circle and drop a perpendicular from C to the given diameter at D. Find CD in terms of AD and BD.
 
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Connect C to A and to B. What kind of triangle is triangle ABC?
 
An easier way: Let O be the centre of the circle. Then OC = OA = (AD+BD)/2. Then look at the triangle ODC to find the answer.
 
I understand upto where you have reached but I still can't proceed from there
 
kuruman said:
Connect C to A and to B. What kind of triangle is triangle ABC?

all sides are unequal
 
What do you know about angle ACB?
 

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