**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. |