Find CD in terms of AD and BD using a perpendicular to the diameter

[Maluka8]

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.

 

[kuruman]

Connect C to A and to B. What kind of triangle is triangle ABC?

 

[Gigasoft]

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.

 

[danielsamyx]

I understand upto where you have reached but I still can't proceed from there

 

[danielsamyx]

Connect C to A and to B. What kind of triangle is triangle ABC?

all sides are unequal

 

[LCKurtz]

What do you know about angle ACB?