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Standard IX
Mathematics
Sum of Opposite Angles of a Cyclic Quadrilateral
PQRS is a par...
Question
PQRS is a paralle\log ram. A circle through P, Q is so drawn that intersects PS at A and QR at B. Then, prove that ABRS is a cyclic quadrilateral.
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Q.
In the figure, a quadrilateral
P
Q
R
S
is drawn to circumscribe a circle. Prove that
P
Q
+
R
S
=
P
S
+
Q
R
Q.
The diagonals PR and QS of a cyclic quadrilateral PQRS intersect at X. The tangent at P is parallel to QS. Prove that
PR bisects
∠
QRS.
Q.
A
B
C
D
is a parallelogram A circle through
A
,
B
is so drawn that it is intersects
A
D
at
P
and
B
C
at
Q
Prove that
P
,
Q
,
C
and
D
are concyclic.
Q.
Question 4
ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.
Q.
The diagonals PR and QS of a cyclic quadrilateral PQRS intersect at X. The tangent at P is parallel to QS. Prove that
P
Q
=
P
S
.
If m
∠
P
Q
S
=
50
o
, then m(
∠
P
R
S
) is
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