MathDB

\vartriangle ABC

is right with

\angle C = 90^o

. The internal angle bisectors of

\angle A

and

\angle B

meet at point

D

, while the external angle bisectors of

\angle A

and

\angle B

meet at point

E

. Suppose that

AD = 1

and

BD = 2

. The value of

DE^2

can be expressed as

x+y \sqrt{z}

for integers

x

y

, and

z

, where

z

is greater than

1

and not divisible by the square of any prime. Compute

100x + 10y + z

. Note: For a generic triangle

\vartriangle PQR

, if we let

Q'

be the reflection of

Q

over

P

, then the external angle bisector of

\angle P

is the line that contains the internal angle bisector of

\angle Q'PR

Problem Statement