MathDB

Trig Geometry

Source: PRMO Leg 2 P22

August 25, 2019

trigonometrygeometryPRMO

Problem Statement

In parallelogram

ABCD

,

AC=10

and

BD=28

. The points

K

and

L

in the plane of

ABCD

move in such a way that

AK=BD

and

BL=AC

. Let

M

and

N

be the midpoints of

CK

and

DL

, respectively. What is the maximum walue of

\cot^2 (\tfrac{\angle BMD}{2})+\tan^2(\tfrac{\angle ANC}{2})

?

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