Given ABCD is a cyclic quadrilateral. Angle ADB = Angle ACB (Angle subtended by chord on the same side of arc) Angle DAC = Angle DBC (Angle subtended by chord on the same side of arc) ⇒ Triangles AED and BEC are similar triangles Similarly triangles AEB and DEC are also similar using AA similarity property. Now, given that AB:CD=2:1 and BC:AD=5:4 AE∕BE=AD∕BC=4∕5 (Similar Triangles AED and BEC ) BE∕CE=AB∕CD=2∕1 (Similar Triangles AEB and DEC) Multiplying both, we get AE∕CE=8∕5.