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

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To find CD in terms of AD and BD, consider triangle ABC formed by connecting points A, B, and C on the circle with diameter AB. The center O of the circle is equidistant from points A and B, leading to OC = OA = (AD + BD)/2. Analyzing triangle ODC, where D is the foot of the perpendicular from C to AB, helps in deriving the relationship. Triangle ABC is scalene, indicating all sides are unequal, which affects angle ACB's properties. Understanding these relationships is crucial for completing the proof.
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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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