Project:Sandbox

$$\\ 1.\ \overline{QO} = \overline{PO}\ (radii) \\ 2.\ \overline{QN} = \overline{PN}\ (perpendicular\ from\ centre\ bisects\ chord\ QP) \\ 3.\ \triangle QNO \cong \triangle PNO (SSS:\ 1.,\ 2.,\ \overline{NO}\ shared) \\ \begin{align*} 4.\ \angle QON  & = 90-\theta\ \\ & = 90 - \theta \end{align*} \\ \begin{align*}5.\ \angle PON = \angle QON\\ (corresp.\ \angle s\ of\ cong.\ \triangle s) \end{align*}$$