Triangle ABC has side lengths 9 cm, 40 cm and 41 cm. A student wishes to decide whether the triangle contains a right angle but is unsure how to begin.
a. (i) Explain, with reason, which of the three given side lengths must be examined first when checking whether triangle ABC is right-angled using only the side lengths.
b. (ii) Write the mathematical condition involving the squares of the three side lengths that must hold true for triangle ABC to be right-angled.
c. (iii) Without performing any calculation, state at which vertex the right angle would lie if the condition written in part (ii) is satisfied.