It is known that in the triangle ABC, the angle bisector ad of ∠ BAC intersects BC with D. It is proved that AC ratio AB equals CD ratio dB

It is known that in the triangle ABC, the angle bisector ad of ∠ BAC intersects BC with D. It is proved that AC ratio AB equals CD ratio dB

Be is perpendicular to ad through B, CF is perpendicular to ad through C
Because ∠ bad = ∠ CAD, ∠ bea = ∠ CFA = 90 degrees
So Bae is similar to CAF → AB / AC = be / CF (1)
Because ∠ BDE = ∠ CDF, ∠ BDE = ∠ CDF = 90 degrees
So triangle BDE is similar to triangle CDF → be / CF = BD / CD 2
AB / AC = BD / CD