Answer:
Step-by-step explanation:
Given that Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC.Then,
AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:
[tex]\frac{BE}{CE}=\frac{BA}{AC}=\frac{c}{b}[/tex]
⇒[tex]\frac{BE}{CE}=\frac{c}{b}[/tex]
⇒[tex]\frac{BE}{BC}=\frac{c}{c+b}[/tex]
Also, ΔDBE is similar to ΔABC, then
[tex]DE=(\frac{BE}{BC})AC[/tex]
=[tex](\frac{c}{c+b})b[/tex]
Therefore, the length of the rhombus is =[tex](\frac{c}{c+b})b[/tex]
