ABCD is a cyclic quadrilateral- The angle bisector of - A - - B - - C and - D intersect at P - Q - R and S as shown in the figure- These four points form quadrilateral PQRS- Quadrilateral PQRS is a -A- cyclic quadrilateralB- rhombusC- squareD- rectangle

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ABCD is a cyc...

Question

ABCD is a cyclic quadrilateral. The angle bisector of $∠ A, ∠ B, ∠ C a n d ∠ D$ intersect at P, Q, R and S as shown in the figure. These four points form a quadrilateral PQRS. Quadrilateral PQRS is a :

square

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rhombus

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rectangle

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cyclic quadrilateral

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Solution

The correct option is D cyclic quadrilateral
Take any value for angle A, B, C, D for the cyclic quadrilateral.
On solving you will find the the opposite angles of the quadrilateral PQRS formed are supplementary to each other.
Hence, PQRS is a cyclic quadrilateral.

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Similar questions

Q. Question 7
If bisectors of

A ∠

and

∠ B

of a quadrilateral ABCD intersect each other at P, of

∠ B

and

∠ C

at Q , of

∠ C

and

∠ D

at R and of

∠ D

and

∠ A

at S, then PQRS is a
(A) rectangle
(B) rhombus
(C) parallelogram
(D) quadrilateral whose opposite angles are supplementary

If bisectors of $∠ A a n d ∠ B$ of a quadrilateral ABCD intersect each other at P, of $∠ B a n d ∠ C$ at Q, of $∠ C a n d ∠ D$ at R and of $∠ D a n d ∠ A$ at S then PQRS is a

(a) rectangle

(b) parallelogram

(d) quadrilateral whose opposite angles are supplementary

Q. If bisectors of

∠ A

and

∠ B

of a quadrilateral

A B C D

intersect each other at

P,

∠ B

and

∠ C

Q .

∠ C

and

∠ D

R,

∠ D

and

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S

then show that

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is a quadrilateral whose opposite angle are supplementary

Q. If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a quadrilateral whose opposite angles are __________.

Q. If bisectors of

∠ A

and

∠ B

of a quadrilateral ABCD intersect each other at

P

, bisectors of

∠ B

and

∠ C

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, bisectors of

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and

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and bisectors of

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ABCD is a cyclic quadrilateral. The angle bisector of ∠A, ∠B, ∠C and ∠D intersect at P, Q, R and S as shown in the figure. These four points form a quadrilateral PQRS. Quadrilateral PQRS is a :

The correct option is D cyclic quadrilateralTake any value for angle A, B, C, D for the cyclic quadrilateral. On solving you will find the the opposite angles of the quadrilateral PQRS formed are supplementary to each other. Hence, PQRS is a cyclic quadrilateral.

ABCD is a cyclic quadrilateral. The angle bisector of $∠ A, ∠ B, ∠ C a n d ∠ D$ intersect at P, Q, R and S as shown in the figure. These four points form a quadrilateral PQRS. Quadrilateral PQRS is a :

The correct option is D cyclic quadrilateral
Take any value for angle A, B, C, D for the cyclic quadrilateral.
On solving you will find the the opposite angles of the quadrilateral PQRS formed are supplementary to each other.
Hence, PQRS is a cyclic quadrilateral.