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

  • Thread starter Thread starter Maluka8
  • Start date Start date
  • Tags Tags
    Geometry Proofs
AI Thread Summary
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.
Maluka8
Messages
2
Reaction score
0
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.
 
Physics news on Phys.org
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?
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Find the equation of the straight line
Replies
4
Views
1K
If two vertices of a square on the same side AB are A(1,2) and B(2,4)....
Replies
2
Views
2K
1st year high school geometry proof
Replies
14
Views
1K
Prove the Extended Law of Sines
Replies
1
Views
2K
ABCD forms a rectangle. With 3 points, A,B,C, find D.
Replies
7
Views
2K
Find the Area of the Shaded Section in a Circle
Replies
12
Views
2K
Parallelogram area (coordinates)
Replies
8
Views
3K
Analysis 1 Homework Help with Complex Numbers
Replies
7
Views
1K
Geometry - Help with theorem proof please
Replies
20
Views
3K
How Do You Solve for t When Point E Lies on Line CD?
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top