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High School Mathematics - 2
8.3 Cyclic Quadrilateral
Cyclic Quadrilateral
: A quadrilateral whose vertices lie on the circumference of a circle is called
cyclic quadrilateral
.
Theorem
: Opposite angles of a cyclic quadrilateral are supplementary.
Proof
:
Directions: Solve the following.
Q 1
: Prove that the exterior angle of a cyclic quadrilateral is equal to its interior opposite angle.
Answer:
Q 2
: Prove that when a parallelogram is inscribed in a circle it becomes a rectangle
Answer:
Q 3
: A pair of opposite sides of a cyclic quadrilateral is equal. Prove that their diagonals are equal.
Answer:
Q 4
: PQRS is a cyclic quadrilateral whose diagonals intersect at A.If ang SQR = 80
^{o}
, angle QPR = 30
^{o}
, find angle SRQ.
80
^{o}
70
^{o}
90
^{o}
Q 5
: PQRS is a cyclic quadrilateral, if angleQ = angleR = 65
^{o}
, find angle P and angle S.
115
^{o}
100
^{o}
120
^{o}
Q 6
:
Answer:
Q 7
:
Answer:
Q 8
:
Answer:
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