Rhombus adef is inscribed into a triangle abc so that they share angle a and the vertex e lies on the side bc . what is the length of the side of the rhombus if ab=c, and ac=b.

Length of side of rhombus is  

Step-by-step explanation:

Given Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC. We have to find the length of side of rhombus.

It is also given that AB=a and AC=b

Let side of rhombus is x.

In ΔCEF and ΔCBA

∠CEF=∠CBA        (∵Corresponding angles)

∠CFE=∠CAB        (∵Corresponding angles)

By AA similarity rule, ΔCEF~ΔCBA

∴ their sides are in proportion

⇒

⇒

⇒

⇒

Hence, length of side of rhombus is  

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .