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T O P I C    R E V I E W
daimath Posted - 07/13/2013 : 02:28:37
Start with a triangle ABC with angle ACB =
Then length AB = tan x length AC

So far so good.

But assume that C is at the center of a circle with a radius of AC and that line AD is drawn so that D is at the intersection of line BC and the circumference of the circle.

How does one calculate the length of AD by reference to the length of AC and the angle ?

(It would have been nice to have been able to add a diagram to illustrate the problem but I can't see how to do that.)
3   L A T E S T    R E P L I E S    (Newest First)
daimath Posted - 07/14/2013 : 06:23:22
Thanks Ultraglide. Your answer is much appreciated.
Ultraglide Posted - 07/13/2013 : 23:59:59
I will make one assumption - the point D is not on the same side of AB as the centre C. Note that DC is a radius and is equal to AC and is the angle between DC and AC. Using the Law of Cosines, cos = (DC+AC-AD)/(2DC.AC). Rearranging, AD = DC + AC - 2DC.ACcos. Since AC=DC. AD = 2AC- 2ACcos which gives:

AD = AC(2(1-cos)
daimath Posted - 07/13/2013 : 20:17:11
Sorry! I should have made it clear that triangle ABC is a right angled triangle with the lines AB and AC subtending the right angle.

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