Given: LI tangent to circle k(O) at I LJ tangent to circle k(O) at J Prove: LO bisects ∠ILJ
By tangent properties,
IL = IJ --- (1)
Also LO = LO --- (2) (obvious)
Also IO and JO are both radii, so IO = JO --- (3)
By (1), (2), and (3), and using SSS postulate, \(\triangle LIO \cong \triangle LJO\).
Therefore \(\angle ILO = \angle JLO\)
\(\implies \) LO bisects ∠ILJ