It is given in the question that:

AD and BC are equal perpendiculars to AB

To prove: CD bisects AB

Proof: In

∠A = ∠B (Perpendicular)

∠AOD = ∠BOC (Vertically opposite angle)

AD = BC (Given)

Therefore,

By AAS congruence,

Now,

AO = OB (By c.p.c.t)

CD bisects AB