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Problem
Problem
In a
Δ
A
B
C
\Delta ABC
Δ
A
B
C
,
r
A
,
r
B
,
r
C
r_A, r_B, r_C
r
A
,
r
B
,
r
C
are the radii of the circles which touch the incircle and the sides emanating from the vertices
A
,
B
,
C
A, B, C
A
,
B
,
C
respectively. Prove that,
r
A
r
B
+
r
B
r
C
+
r
C
r
A
=
r
\sqrt{r_A r_B} + \sqrt{r_B r_C} + \sqrt{r_C r_A} = r
r
A
r
B
+
r
B
r
C
+
r
C
r
A
=
r
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