Question Number 49430 by [email protected] last updated on 06/Dec/18
Commented by [email protected] last updated on 07/Dec/18
![DA^ E=𝛉,AD=r . there is two equilateral triangles, inscribed in circle ,one vertex on point:C and two anothers locate on circle′s premeter.[one side⊥BC] find side of this triangels in terms of :r ,𝛉 . [C,is the midpoint of :ED and B,A,C are collinear.]](Q49431.png)
$${D}\overset{ } {{A}E}=\boldsymbol{\theta},{AD}=\boldsymbol{{r}}\:\:\:. \\ $$$${there}\:{is}\:{two}\:{equilateral}\:{triangles}, \\ $$$$\:{inscribed}\:{in}\:{circle}\:,{one}\:{vertex}\:{on}\: \\ $$$${point}:{C}\:{and}\:{two}\:{anothers}\:{locate}\:{on} \\ $$$${circle}'{s}\:\:{premeter}.\left[{one}\:{side}\bot{BC}\right] \\ $$$${find}\:{side}\:{of}\:{this}\:{triangels}\:{in}\:{terms} \\ $$$${of}\::\boldsymbol{{r}}\:,\boldsymbol{\theta}\:. \\ $$$$\left[{C},{is}\:{the}\:{midpoint}\:{of}\::{ED}\:{and}\:{B},{A},{C}\right. \\ $$$$\left.{are}\:{collinear}.\right] \\ $$