In the ABCD rectangle: AB = 6cm; AC = 10 cm; О is the point of intersection of the diagonals; perpendicular BN is dropped

In the ABCD rectangle: AB = 6cm; AC = 10 cm; О is the point of intersection of the diagonals; perpendicular BN is dropped onto the diagonal. Find the segments into which the diagonal AC of the points H and O is divided

Because absd – rectangle, the point of intersection of the diagonals divides them in half. hence ao = bo = 5 cm. Consider a triangle abo. ab = 6cm, bo = 5cm. bn divides a triangle into two rectangular ones and is a leg in them. let an = 5 – x, but = x. hence bn ^ 2 = 36 – (5 – x) ^ 2 = 25 – x ^ 2
36 – 25 + 10x – x ^ 2 = 25 – x ^ 2
10x = 14
x = 1.4
Answer: o divides ac into segments ao = oc = 5 cm, n divides ac into segments an = 3.6 cm and ns = 6.4 cm.