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Byju's Answer
Standard XII
Mathematics
Length of Internal Common Tangent
Prove that, t...
Question
Prove that, tangents drawn to the end points of diameter of the circle are parallel to each other.
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Solution
Given:
A
B
is the diameter of the circle with center
O
.
Two tangents
P
Q
and
R
S
are drawn at points
B
and
A
respectively.
Proof:
The radius is perpendicular to these tangents.
That is,
O
A
⊥
R
S
and
O
B
⊥
P
Q
⇒
∠
O
A
R
=
∠
O
A
S
=
∠
O
B
P
=
∠
O
B
Q
=
90
o
∴
∠
O
A
R
=
∠
O
B
Q
(Alternate interior angles)
∴
∠
O
A
S
=
∠
O
B
P
(Alternate interior angles)
Since alternate interior angles are equal, lines
P
Q
and
R
S
are parallel.
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Q.
Prove that the tangents drawn at the ends of a diameter ofa circle are parallel.