MathDB

Junior Regional Olympiad - FBH 2014 Grade 7 Problem 3

Source:

October 3, 2018

geometrytrapezoid

Problem Statement

Let

ABCD

be a trapezoid with base sides

AB

and

CD

and let

AB=a

BC=b

CD=c

DA=d

AC=m

and

BD=n

. We know that

m^2+n^2=(a+c)^2

a)

Prove that lines

AC

and

BD

are perpendicular

b)

Prove that

ac<bd