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Byju's Answer
Standard X
Mathematics
Sum of Opposite Sides Are Equal in a Quadrilateral Circumscribing a Circle
In the figure...
Question
In the figure (i) given below, the sides of the quadrilateral touch the circle Prove that
A
B
+
C
D
=
B
C
+
D
A
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Solution
Lengths of the tangents from an external point are equal.
A
P
=
A
S
,
B
P
=
B
Q
,
C
R
=
C
Q
and
D
R
=
D
S
A
B
+
C
D
=
(
A
P
+
B
P
)
+
(
C
R
+
D
R
)
=
A
S
+
B
Q
+
C
Q
+
D
S
=
(
A
S
+
D
S
)
+
(
B
Q
+
C
Q
)
=
A
D
+
B
C
Hence
A
B
+
C
D
=
A
D
+
B
C
.
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