Trig problem help please

[apple2357]

I have an approach ( see hint below if interested) but wonder if there are different approaches to this problem? It feels like there should be?



My approach below this line:

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By dropping a perpendicular from the centre of the circle to the tangent line and using a mixture of right angled triangle ideas and then sine rule on the non right angled triangle.

 

[Dr.Peterson]

Your idea agrees with my idea.

There are usually multiple methods, but in this case nothing else jumps out at me -- at least, nothing that seems likely to be better.

 

[apple2357]

Thanks for considering it!