MathDB

Let

ABCD

be a trapezium with bases

AB

and

CD

such that

AB = 2 CD

. From

A

the line

r

is drawn perpendicular to

BC

and from

B

the line

t

is drawn perpendicular to

AD

. Let

P

be the intersection point of

r

and

t

. From

C

the line

s

is drawn perpendicular to

BC

and from

D

the line

u

perpendicular to

AD

. Let

Q

be the intersection point of

s

and

u

. If

R

is the intersection point of the diagonals of the trapezium, prove that points

P, Q

and

R

are collinear.

Problem Statement