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Mathematics
Mathematics
Problem
In a circle with center
O
O
O
, two tangents
T
P
TP
T
P
and
T
Q
TQ
T
Q
are drawn from an external point
T
T
T
. Prove that
∠
P
T
Q
\angle PTQ
∠
P
T
Q
is double
∠
O
P
Q
\angle OPQ
∠
O
P
Q
(where
P
P
P
and
Q
Q
Q
are points of contact). Using this relationship, if
∠
O
P
Q
\angle OPQ
∠
O
P
Q
is
25
∘
25^{\circ}
2
5
∘
, find
∠
P
T
Q
\angle PTQ
∠
P
T
Q
.
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