Thread: trisecting diagonal

ABCD is a cyclic quadrilateral such that AB is 7 , BC is 24 , CD is 15 and DA is 20 units respectively. points E and F lie on AC such that AE=EF=FC . what is the area of the quadrilateral BEDF.

Originally Posted by geniusgarvil

ABCD is a cyclic quadrilateral such that AB is 7 , BC is 24 , CD is 15 and DA is 20 units respectively. points E and F lie on AC such that AE=EF=FC . what is the area of the quadrilateral BEDF.

1. By first inspection:



That means AC = 25 and ABCD consists of 2 right triangles with a common hypotenuse.

2. The long way: In a cyclic quadrilateral the interior angles of opposite vertices add up to 180° (or pi).

Use Cosine rule:





Solve this system of equations for x and AC.

3. Let a denote the area. Then