Sine of angle between direct common tangents of two circles? This is a question I found: Given two circles intersecting orthogonally having the length of common chord 24/5 units the radius of one of the circles is 3 units then what is the sine of the angle between the direct common tangents? The answer given is 4√6/25. How do I approach this problem? I know that direct common tangents meet at a point that externally divides line joining centres of circles in ratio of their radii, but I am getting negative values when I try to solve this. How do I do this?

To make things simpler. There's this formula you can memorise or derive as you may like by similarity and Pythagoras. 
Alpha{angle between DCT}= 2sin^-1[|r2-r1|/ d] 
Where R1 and R2 are radii and d is distance between centres.
Here, sin a/2 comes out to be 1/5.
Thus sin a = 2 sin a/2 cos a/2
= 4✓6/25
