Prove that if ∠C = 90°, then
(a) the segments AAb and CCb, as well as BBa and CCa are congruent and perpendicular;
(b) segments AAb, BBa and the altitude CHc concur;
(c) segments BcCb and AOa, where Oa is the center of the square BCAcAb, concur with BBa and CCa;
(d) BcCb and AOa are perpendicular.
Find the ratio BcCb / AOa.
Which of statements (a) – (d) remain true for an arbitrary triangle? How to prove them?