Discussion Question 2 (Solution)

Download the GeoGebra file: http://www.geogebratube.org/material/download/format/file/id/42710


\[OA = OB{\rm{\;(radii\;of\;circle)}}\]
\[\angle AOQ = \angle BOQ{\rm{\;(tangents\;from\;ext\;pt)}}\]
\[OQ = OQ{\rm{\;(common)}}\]
\[\therefore \Delta AOQ \equiv \Delta BOQ{\rm{\;(SAS)}}\]
\[{\rm{Hence,}}\; \angle AQO = \angle BQO{\rm{\;(corr\;\angle {\rm{s}}\;of\;congruent\;}}\Delta {\rm{s)}}\]
\[\angle AQO + \angle BQO = 180^\circ {\rm{\;(adj\;}}\angle {\rm{s\;on\;a\;str\;line)}}\]
\[2\angle AQO = 180^\circ \]
\[\angle AQO = 90^\circ \]
\[\therefore \angle AQP = 90^\circ {\rm{\;(adj\;}}\angle {\rm{s\;on\;a\;str\;line)}}\]