iran-konkur 2018 Q129

iran-konkur · Other · konkur-riazi_1397_specialized Circles Tangent Lines and Tangent Lengths
129. In the figure below, $AD$ is tangent to the circle with center $O$, and $OH$ is perpendicular to $AC$. If $\widehat{DBC} = 2\widehat{DAC}$, how many times is angle $\widehat{COH}$ equal to angle $\widehat{DAC}$?
\begin{minipage}{0.45\textwidth} [Figure: Circle with center $O$, tangent line $AD$, points $B$, $C$, $H$ marked] \end{minipage} \begin{minipage}{0.45\textwidth} \begin{flushright} (1) $2.5$
(2) $3$
(3) $3.5$
(4) $4$ \end{flushright} \end{minipage}
\textbf{129.} In the figure below, $AD$ is tangent to the circle with center $O$, and $OH$ is perpendicular to $AC$. If $\widehat{DBC} = 2\widehat{DAC}$, how many times is angle $\widehat{COH}$ equal to angle $\widehat{DAC}$?

\begin{minipage}{0.45\textwidth}
\textit{[Figure: Circle with center $O$, tangent line $AD$, points $B$, $C$, $H$ marked]}
\end{minipage}
\hfill
\begin{minipage}{0.45\textwidth}
\begin{flushright}
(1) $2.5$

(2) $3$

(3) $3.5$

(4) $4$
\end{flushright}
\end{minipage}