D is a point

In quadrilateral, NDMB,

BND = 90, NBM = 90, BMD = 90, and hence MDN = 90,

It could be a square or rectangle,

Hence DN = BM, DM = NB,

BDC, using Pythagorus's theorem,

DB² + DC² = BC²

DB² + DC² = (BM+MC)²

DB² + DC² = (DN+MC)²

DB² + DC² = DN² + MC² +2DN MC

DB² - DN² + DC² - MC² = 2DN MC

DM² + DM² = 2DN MC

DM² = DN.MC

Regards,

Team,

TopperLearning.