Given: AB=AC

To prove: AD>AC

Proof:

In ∆ABC,

∠ACD = ∠B + ∠BAC

= ∠ACB + ∠BAC …as ∠C = ∠B as AB = AC

= ∠CAD + ∠CDA +∠BAC …as ∠ACB = ∠CAD + ∠CDA

∴∠ACD > ∠CDA

So the side opposite to ∠ACD is the longest

∴AD > AC