Problem

Problem

Let points

P_1, P_2, P_3, \dots, P_{n-1}

divide the side

BC

of

\Delta ABC

into

n

parts. Let

r_1, r_2, r_3, \dots, r_n

be the radii of inscribed circles and let

p_1, p_2, \dots, p_n

be the radii of excircles corresponding to vertex

A

for triangles

ABP_1, AP_1P_2, \dots, AP_{n-1}C

, and let

r

and

p

be the corresponding radii for the triangle

ABC

. Show that

\frac{r_1}{p_1}\cdot\frac{r_2}{p_2}\cdots\frac{r_n}{p_n}=\frac{r}{p}.

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