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Byju's Answer
Standard X
Mathematics
Intersection between Tangent and Secant
In the given ...
Question
In the given figure, two circles intersect each other at points S and R. Their common tangent PQ touches the circle at points P, Q. Prove that,
∠
P
R
Q
+
∠
P
S
Q
=
180
o
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Solution
REF.Image.
∠
P
R
Q
+
∠
P
S
Q
=
180
∘
∠
S
P
Q
=
1
2
m
(
a
r
c
P
R
)
∠
S
Q
R
=
1
2
m
(
a
r
c
P
Q
)
Inscribed angle
∠
P
S
Q
+
∠
P
Q
S
+
∠
S
Q
P
=
180
∘
(sum of all angle)
∠
S
Q
R
=
1
2
×
m
(
a
r
c
S
R
Q
)
also
∠
S
P
Q
=
1
2
m
(
a
r
c
S
R
P
)
But
∠
P
S
Q
=
1
/
2
∠
P
R
Q
a
r
c
P
R
+
a
r
c
R
Q
=
180
∘
also
∠
P
R
Q
+
∠
P
S
Q
=
180
∘
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Similar questions
Q.
In the given figure, two circles intersect each other at points S and R. Their common tangent PQ touches the circle at points P, Q.
Prove that, ∠ PRQ + ∠ PSQ = 180°