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National and Regional Contests
Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2013 Saudi Arabia Pre-TST
2.4
2.4
Part of
2013 Saudi Arabia Pre-TST
Problems
(1)
triangle area criterion for right triangle with excenters, 1/2 AI_b AI_c.
Source: 2013 Saudi Arabia Pre-TST 2.4
9/13/2020
△
A
B
C
\vartriangle ABC
△
A
BC
is a triangle and
I
b
.
I
c
I_b. I_c
I
b
.
I
c
its excenters opposite to
B
,
C
B,C
B
,
C
. Prove that
△
A
B
C
\vartriangle ABC
△
A
BC
is right at
A
A
A
if and only if its area is equal to
1
2
A
I
b
⋅
A
I
c
\frac12 AI_b \cdot AI_c
2
1
A
I
b
⋅
A
I
c
.
geometry
excenter
area of a triangle