MathDB

Bash? Anyone??

Source: BdMO 2024 Secondary National P7 Higher Secondary National P2

March 18, 2024

geometryperpendicular linescartesian coordinates

Problem Statement

Let

ABCD

be a square.

E

and

F

lie on sides

AB

and

BC

, respectively, such that

BE = BF

. The line perpendicular to

CE

, which passes through

B

, intersects

CE

and

AD

at points

G

and

H

, respectively. The lines

FH

and

CE

intersect at point

P

and the lines

GF

and

CD

intersect at point

Q

. Prove that the line

DP

is perpendicular to the line

BQ

.

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