(1) angle BEC= angle CDB=90 degrees, angle ABC= angle ACB, BC=CB, △ BDC △ CEB (AAS), so BE=CD, angle EBC= angle DCB.

Because AB=AC and AD=AE.

(2) Extend AO to BC in F ..

AO=AO, AD=AE, angle AEB= angle ADC = 90 degrees, △ oad △ OAE (H. L), so angle DOA= = angle EOA, because angle DOB= = angle EOC, so angle BOF= angle COF, because angle EBC= angle DCB.

So OA is perpendicular to BC.