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2022 JHMT HS
9
Ratio Involving Convex Quadrilateral Side Lengths
Ratio Involving Convex Quadrilateral Side Lengths
Source:
August 8, 2024
geometry
2022
Problem Statement
In convex quadrilateral
K
A
L
E
KALE
K
A
L
E
, angles
∠
K
A
L
\angle KAL
∠
K
A
L
,
∠
A
K
L
\angle AKL
∠
A
K
L
, and
∠
E
L
K
\angle ELK
∠
E
L
K
measure
11
0
∘
110^\circ
11
0
∘
,
5
0
∘
50^\circ
5
0
∘
, and
1
0
∘
10^\circ
1
0
∘
, respectively. Given that
K
A
=
L
E
KA = LE
K
A
=
L
E
and that
K
L
‾
\overline{KL}
K
L
and
A
E
‾
\overline{AE}
A
E
intersect at point
X
X
X
, compute the value of
K
X
2
A
L
⋅
E
X
\tfrac{KX^2}{AL\cdot EX}
A
L
⋅
EX
K
X
2
.
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