AB and AC are two chords of a circle and the diameter passing through 'A' bisects the angle ∠BAC. Prove that AB = AC.
 

Given: AD is angle bisector of ∠A,
Construction: Join BD and DC. 
Proof:  In ΔABD and ΔACD,
AD = AD
∠DAC = ∠DAB          (AD is angle bisector of ∠A) 
∠ACD = ∠ABD = 90° [Angle in semi-circle is 90°]
∴ ∠ABD ≅ ΔACD 
   � = AC (C.P.C.T.E.)