Triangles formed by lines passing through ends of two chords with a ratio of 1:3

This question was uploaded on 14/01/22 on social media accounts.

Solution:

BCED is a cyclic quadrilateral, its opposite angles are supplementary by this, ABC and AED are similar triangles.

Given, BC:ED = 1:3

So, AB:AE = AC:AD = 1:3

Let area of triangle ABC is 'A' then area of triangle AED will be '9A'.

Now, Red = A,

Blue = 9A - Red = 8A

Red/Blue = 1/8