Quadrilateral ABCD is inscribed in a circle. Find the length of its shorter diagonal if AB=12, CD=18, arc BC=120, and arc AD =60°.

Answer 1

Since arcs BC+AD = 180°, and 18:12 = 3/2,
arc CD=3x and arc AB=2x, so 5x=180 and x=36

So, arc AB=72° and arc CD=108°

Now you can use that to analyze ABCD, knowing the angles and lengths of all the sides.