Theorem on Cyclic Quadrilateral and Its Converse
Trending Questions
Q. If PQRS is a cyclic quadrilateral in which ∠PSR=70∘ and ∠QPR=40∘, then find ∠PRQ.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1774081/original_1.PNG)
Q.
Find x, y and z in the figure given below.
x=70∘, y=110∘, z=70∘
x=110∘, y=110∘, z=70∘
x=110∘, y=110∘, z=90∘
x=110∘, y=110∘, z=110∘
Q. ![](https://search-static.byjusweb.com/question-images/byjus/ckeditor_assets/pictures/908377/original_Byjus_Classes_test_20_7.png)
Find the value of 𝑥 in the given figure.
![](https://search-static.byjusweb.com/question-images/byjus/ckeditor_assets/pictures/908377/original_Byjus_Classes_test_20_7.png)
Find the value of 𝑥 in the given figure.
- 50∘
- 55∘
- 65∘
- 60∘
Q. PQRS is a cyclic quadrilateral. If ∠Q=∠R=65∘, then find ∠P= ___ and ∠S = __.
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/481763/original_65_degrees_each.png.png)
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/481763/original_65_degrees_each.png.png)
- 120∘, 110∘
- 115∘, 115∘
- 125∘, 115∘
- 115∘, 125∘
Q. ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If ∠ADC=130∘, then find ∠BAC.
- 25∘
- 60∘
- 50∘
- 40∘
Q.
What is the sum of either pair of opposite angles of a cyclic quadrilateral?
90°
180°
360°
45°
Q. In the given figure, A, B and C are three points on the circle with centre O such that ∠BOC=30∘ and ∠AOB=60∘. If D is a point on the circle that is not on the arc ABC, then find ∠ABC.
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/548007/original_Annotation_28129.png)
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/548007/original_Annotation_28129.png)
- 135∘
- 45∘
- 120∘
- (602)∘
Q. In the given figure, what is the value of x ?
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/474606/original_274559.png)
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/474606/original_274559.png)
- 30∘
- 20∘
- 15∘
- 10∘
Q. In the given figure, ABCD is a cyclic quadrilateral, AE is drawnn parallel to CD and BA is produced. If ∠ABC=92∘ and ∠FAE=20∘, then ∠BCD is equal to
![1460573_17e4c608e5374cab82258411956a9f41.JPG](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/1460573_17e4c608e5374cab82258411956a9f41.JPG)
Q. In the given figure , AE is the diameter of the circle. Write down the numerical value of ∠ABC+∠CDE.
![271386_6edeb429372c4399b27eded2aa9e7f78.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/271386_6edeb429372c4399b27eded2aa9e7f78.png)
![271386_6edeb429372c4399b27eded2aa9e7f78.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/271386_6edeb429372c4399b27eded2aa9e7f78.png)
- 180∘
- 270∘
- 360∘
- 540∘
Q.
What is the sum of either pair of opposite angles of a cyclic quadrilateral?
90∘
180∘
360∘
45∘
Q.
In the given figure, if ∠AOC=130∘, then the value of ∠ABC = _______.
95∘
115∘
50∘
100∘