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Byju's Answer
Standard X
Mathematics
Tangents from a Given Point
In the given ...
Question
In the given below figure, from an external point P, a tangent PT and a secant PAB is drawn to a
circle with centre O. ON is perpendicular on the chord AB. Prove that PA. PB = PT2.
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Solution
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Similar questions
Q.
In figure,from an external point
P
,a tangent
P
T
and a line segment
P
A
B
is drawn to a circle with centre
O
.
O
N
is perpendicular on the chord
A
B
.
Prove that:-
(
i
)
P
A
.
P
B
=
P
A
2
−
A
N
2
(
i
i
)
P
N
2
−
A
N
2
=
O
P
2
−
O
T
2
(
i
i
i
)
P
A
.
P
B
=
P
T
2
Q.
If
P
A
B
is a secant to a circle of centre
O
intersecting the circle of
A
and
B
and
P
T
is tangent segment, then prove that-
P
A
×
P
B
=
P
T
2
Q.
From an external point
P
, a tangent
P
T
and a line segment
P
A
B
are drawn to a circle with center
O
. Prove that
P
A
.
P
B
=
P
T
2
Q.
In the given figure,
P
A
and
P
B
are two tangents drawn from an external point
P
to a circle with centre
O
. Prove that
O
P
is the right bisector of line segment
A
B
.
Q.
From an external point P, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the perpendicular bisector of AB.
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