MathDB

4

Part of 2003 Bosnia and Herzegovina Junior BMO TST

Problems(1)

a + c < b + d, ac < bd in trapezoid with m^2 + n^2 = (a + c)^2

Source: 2003 Bosnia & Herzegovina JBMO TST p4

5/27/2020
In the trapezoid ABCDABCD (AB∥DCAB \parallel DC) the bases have lengths aa and cc (c<ac < a), while the other sides have lengths bb and dd. The diagonals are of lengths mm and nn. It is known that m2+n2=(a+c)2m^2 + n^2 = (a + c)^2. a) Find the angle between the diagonals of the trapezoid. b) Prove that a+c<b+da + c < b + d. c) Prove that ac<bdac < bd.
geometrytrapezoidgeometric inequality