Suppose there is given right triangle($AC=6$) and circle (radius$=5$) which goes through $A$ and $C$ and meets $AB$ leg at the midpoint. Here is picture
We are asked to find length of leg.in my point of view, we can connect center of circle with $A$ and $C$ point,get isosceles triangle we know all sides ,find angle at center, then connect center also to $A$ and $D$ here we know both length (radius) angle will be $180-a$ ($a$ it is which we got by cosine law) calculate $AD$ by the cosine law and got finally $AB$, can you show me shortest way? or am I correct or wrong? Please help!