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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2024 Korea Junior Math Olympiad (First Round)
11.
11.
Part of
2024 Korea Junior Math Olympiad (First Round)
Problems
(1)
Geometry finding area
Source: 2024 KJMO round 1
10/26/2024
There is a square
A
B
C
D
.
ABCD.
A
BC
D
.
P
P
P
is on
A
B
ˉ
\bar{AB}
A
B
ˉ
, and
Q
Q
Q
is on
A
D
ˉ
\bar{AD}
A
D
ˉ
They follow
A
P
ˉ
=
A
Q
ˉ
=
A
B
ˉ
5
\bar{AP}=\bar{AQ}=\frac{\bar{AB}}{5}
A
P
ˉ
=
A
Q
ˉ
=
5
A
B
ˉ
Let
H
H
H
be the foot of the perpendicular point from
A
A
A
to
P
D
ˉ
\bar{PD}
P
D
ˉ
If
∣
△
A
P
H
∣
=
20
|\triangle APH|=20
∣△
A
P
H
∣
=
20
, Find the area of
△
H
C
Q
\triangle HCQ
△
H
CQ
.
geometry
area