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Given: LI tangent to circle k(O) at I LJ tangent to circle k(O) at J Prove: LO bisects ∠ILJ

 Apr 10, 2020
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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

 Apr 14, 2020

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