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In a , , , are the radii of the circles which touch the incircle and the sides…
MATHEMATICS · Subjective · A Level · Mathematics · Proof · Proof
Problem
In a
△
A
B
C
\triangle ABC
△
A
B
C
,
r
A
r_A
r
A
,
r
B
r_B
r
B
,
r
C
r_C
r
C
are the radii of the circles which touch the incircle and the sides emanating from the vertices
A
A
A
,
B
B
B
,
C
C
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
.
Related theory
Circles
Mathematical Logic
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