A) to show angle bisection:
Show both angles are equal:
(ABL = LBC)
Let angle LBC be x
Then BLC = 180 - 90 - x (angles in triangle BCL)
= 90 - x
Angle ALN = BLC (vertically opp angle)

Since AL = AN,
angle ANL = ALN (isosceles triangle LAN)
angle BAN = 90 (radius perpend to tangent )
:. Angle ABL = 180 - 90 - (90-x)
(angles in triangle BAN)
= x
= angle LBC (shown) //

B) Angle BOL = Angle BAN (Corr angle)
= Angle BCL (both 90 deg)
Angle OBL = Angle CBL (from part A)
BL = BL (exact same length)
By AAS test, they are congruent //