Question

Seg $RM$ and seg $RN$ are tangent segments of a circle with centre $O$. Prove that seg $OR$ bisects $\angle MRN$ as well as $\angle MON$.

Answer 1

It is given that $RM$ and $RN$ are the two tangent segments of a circle with centre $O$. Let $OR$ be the segment and from $\Delta MOR$ and $\Delta NOR,$

$MR=NR($ Tangent segments of circle are always equal$)$

$OM=ON($Radius of the circle$)$

$OR=OR$ $($ Common$)$

Therefore by SSS rule of Congruency$,\Delta MOR\cong \Delta NOR$

$\Rightarrow$ By $CPCT,$

$\angle MRO=\angle NRO$

Thus$,$ the segment OR bisects the angle $MRN$

Hence proved$.$