Author 
Topic 

daimath
Junior Member
USA
6 Posts 
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.) 


daimath
Junior Member
USA
6 Posts 
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. 


Ultraglide
Advanced Member
Canada
299 Posts 
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+ACAD)/(2DC.AC). Rearranging, AD = DC + AC  2DC.ACcos. Since AC=DC. AD = 2AC 2ACcos which gives:
AD = AC(2(1cos) 


daimath
Junior Member
USA
6 Posts 
Posted  07/14/2013 : 06:23:22

Thanks Ultraglide. Your answer is much appreciated. 



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