[ The product of the lengths of the chord segments $\underline{\text { and }}$ the lengths of the secant segments ] Complex [The ratio of the areas of triangles with a common base or common height]

Diagonal $A C$ of the convex quadrilateral $A B C D$ is the diameter of the circumscribed circle around it. Find the ratio of the areas of triangles $A B C$ and $A C D$, given that diagonal $B D$ divides $A C$ in the ratio 2:5 (measured from point $A$), and $\angle B A C=45^{\circ}$.
Apply the theorem of the products of segments of intersecting chords.

## Answer

$\frac{29}{20}$.