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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 ACSo 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

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+AC-AD)/(2DC.AC). Rearranging, AD = DC + AC - 2DC.ACcos. Since AC=DC. AD = 2AC- 2ACcos which gives:AD = AC(2(1-cos)

daimath
Junior Member

USA
6 Posts

 Posted - 07/14/2013 :  06:23:22 Thanks Ultraglide. Your answer is much appreciated.
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