# Thread: trigo problem no. 9

1. ## trigo problem no. 9

trigo problem no. 9
p148 q8

How to do [b]? thanks

2. Originally Posted by afeasfaerw23231233
trigo problem no. 9
p148 q8

How to do [b]? thanks
Actually this one's quite annoying me.

I can see a brutal approach - but I'm sure there's a simple approach based on a cyclic quadrilateral theorem (so that there's a point to part (a)) ..... Probably a theorem dealing with the case of one of the diagonals being a diameter of the circle that would lead to something along the lines of $\displaystyle LM = RQ \sin \alpha$ ... perhaps a special case that follows from Ptolemy's Theorem ....... Nothing I could find using google - I'll probably end up proving (or disproving) what I want myself .....

3. thanks! my textbook mentioned it before, but i forget it.
for any triangle, a/sinA = b/sinB = c/sinC = 2R, where R is the radius of the circle, providing that point ABC are concyclic. here's textbook's content about the sine law.
but what is Ptolemy's Theorem? i didn't learn it before