Question

Geometry question

Answer 1

\(\triangle ABC\) is an equilateral triangle . \(O\) os the center.\(O\) lies in the segment \(AD\).

prove that \(AO:OD::2:1\)

Answer 2

\(\large \color{black}{\begin{align} AB^2=AD^2+BD^2\hspace{.33em}\\~\\
BO^2=OD^2+BD^2\hspace{.33em}\\~\\
AO=BO=r\hspace{.33em}\\~\\
\end{align}}\)

Answer 3

how do you know triangle ABD is right triangle ?

Answer 4

that doesnt prove angle D is right angle yet

Answer 5

that just shows that triangle OBC is an isosceles triangle

Answer 6

we can prove that
\(\large \color{black}{\begin{align} \triangle OBD \cong \triangle OCD\hspace{.33em}\\~\\
\end{align}}\)

Answer 7

yes we need to prove that first

Answer 8

\(\large \color{black}{\begin{align} OB &\cong OC\hspace{.33em}\\~\\
\angle OBD &\cong \angle OCD \hspace{.33em}\\~\\
OD&=OD
\end{align}}\)