A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD inte

Question

A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals

Accepted Answer

8 : 5. 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 similari