153 degrees must be a special angle
Chord subtends an angle of at the centre of a circle. Point is the point of trisection of the major arc closer to . If is a point on the minor arc , find in degrees .
The answer is 69.
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1 solution
Because
∠
A
O
B
=
1
5
3
, the other side of
∠
A
O
B
=
3
6
0
−
1
5
3
=
2
0
7
. Point
P
trisects the major arc
A
B
thus
O
P
trisects
∠
A
O
B
. Therefore
∠
B
O
P
=
6
9
, and
∠
P
O
A
=
1
3
8
. By central angle theorem we can tell that
∠
A
Q
P
=
2
1
∠
P
O
A
.
∠
A
Q
P
=
6
9