MathDB
Problems
Contests
National and Regional Contests
India Contests
Postal Coaching
2009 Postal Coaching
5
PA_1 + PA_3 + PA_5 + PA_7 +PA_9 = PA_2 + PA_4 + PA_6 + PA_8 + PA_{10}
PA_1 + PA_3 + PA_5 + PA_7 +PA_9 = PA_2 + PA_4 + PA_6 + PA_8 + PA_{10}
Source: Indian Postal Coaching 2009 set 6 p5
May 26, 2020
equal angles
geometry
angles
Sum
Problem Statement
Let
P
P
P
be an interior point of a circle and
A
1
,
A
2
.
.
.
,
A
10
A_1,A_2...,A_{10}
A
1
,
A
2
...
,
A
10
be points on the circle such that
∠
A
1
P
A
2
=
∠
A
2
P
A
3
=
.
.
.
=
∠
A
10
P
A
1
=
3
6
o
\angle A_1PA_2 = \angle A_2PA_3 = ... = \angle A_{10}PA_1 = 36^o
∠
A
1
P
A
2
=
∠
A
2
P
A
3
=
...
=
∠
A
10
P
A
1
=
3
6
o
. Prove that
P
A
1
+
P
A
3
+
P
A
5
+
P
A
7
+
P
A
9
=
P
A
2
+
P
A
4
+
P
A
6
+
P
A
8
+
P
A
10
PA_1 + PA_3 + PA_5 + PA_7 +PA_9 = PA_2 + PA_4 + PA_6 + PA_8 + PA_{10}
P
A
1
+
P
A
3
+
P
A
5
+
P
A
7
+
P
A
9
=
P
A
2
+
P
A
4
+
P
A
6
+
P
A
8
+
P
A
10
.
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