In △ABC, it is given that AB=AC=10 cm. The altitude from A meets BC at D, so that AD⊥BC.
Use this information to answer the questions below.
(a) Prove that △ABD≅△ACD.
(b) Deduce that D is the midpoint of BC and write the measure of BD. If BC=14 cm, give the numerical value of BD.
(c) Calculate the length of AD. Leave the answer in simplest radical form.