Sum of Opposite Sides Are Equal in a Quadrilateral Circumscribing a Circle
Trending Questions
Q.
The parallelogram circumscribing a circle is a rhombus.
True
False
Q. The perimeter of the given quadrilateral ABCD circumscribing a circle is
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/484669/original_10.png)
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/484669/original_10.png)
- 32 cm
- 62 cm
- 48 cm
Q.
If a quadrilateral ABCD is drawn to circumscribe a circle, then which of the options is true?
AC + AD = BD + CD
AB + CD = BC + AD
AC + AD = BC + DB
AB + CD = AC + BC
Q.
Solve the following:
In fig, quadrilateral ABCD is circumscribing a circle. Find the perimeter of the quadrilateral ABCD.
Q. If the sides of a quadrilateral ABCD touch a circle, then____.
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/477818/original_114.png)
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/477818/original_114.png)
- AB+BC=CD+AD
- AB-CD=BC-AD
- AB+CD=BC+AD
- AB-CD=BC+AD
Q. In the given figure, quadrilateral ABCD is drawn to circumscribe a circle. If AB+CD =15 cm, then find the perimeter of the quadrilateral.
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/477837/original_107.png)
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/477837/original_107.png)
- 30 cm
- 15 cm
- 20 cm
- 35 cm
Q. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC. [ 2 Marks]
Q. Question 5
In figure AB and CD are common tangents to two circles of unequal radii prove that AB=CD
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/14584/content_1.png)
In figure AB and CD are common tangents to two circles of unequal radii prove that AB=CD
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/14584/content_1.png)
Q. In the given figure, a circle is inscribed in a ΔABC, such that it touches the sides AB, BC, and CA at points D, E, and F, respectively. If the lengths of sides AB, BC, and CA are 12 cm, 8 cm, and 10 cm, respectively, find the lengths of AD, BE, and CF.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1746877/original_Picture_1.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1746877/original_Picture_1.png)
Q. A circle is inscribed in a quadrilateral as shown below, then
AB + CD = BC + AD.
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/6881/content_174640.png)
AB + CD = BC + AD.
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/6881/content_174640.png)
- True
- False
Q. A circle is inscribed in a quadrilateral as shown below, then
AB + CD = BC + AD.
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/6881/content_174640.png)
AB + CD = BC + AD.
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/6881/content_174640.png)
- True
- False
Q. In a right-angled ΔABC a circle with side AB as diameter is drawn to intersect the hypotenuse ACin L. Prove that the tangent to the circle at L bisects the side BC.
Q. Question 2
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.
Q. If the sides of a quadrilateral ABCD touch a circle, then prove that AB+CD=BC+AD
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/477818/original_114.png)
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/477818/original_114.png)
Q. The perimeter of the given quadrilateral ABCD circumscribing a circle is
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/484669/original_10.png)
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/484669/original_10.png)
- 32 cm
- 62 cm
- 48 cm
Q. A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD=AD=BC.
![1366230_b41aa9901c4d41f887e817fb3d2d7f3b.PNG](https://search-static.byjusweb.com/question-images/toppr_ext/questions/1366230_b41aa9901c4d41f887e817fb3d2d7f3b.PNG)
Q.
Solve the following:
In fig, quadrilateral ABCD is circumscribing a circle. Find the perimeter of the quadrilateral ABCD.
Q. Match the following:
- AP + DR = 5 cm
- DC = 7 cm
- DC = 9 cm
Q. In the given figure, a circle touches all the four side of quadrilateral ABCD with AB=6 cm, BC=7 cm and CD=4 cm. Find AD.
![971301_4dde0bb8147b4f82a1abfcec0e6237a4.png](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/971301_4dde0bb8147b4f82a1abfcec0e6237a4.png)
![971301_4dde0bb8147b4f82a1abfcec0e6237a4.png](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/971301_4dde0bb8147b4f82a1abfcec0e6237a4.png)
Q. ABCD is a rectangle. Taking AD as a diameter, a semicircle AXD is drawn which intersects the diagonal BD at X. If AB=12cm, AD=9cm, T he values of BD and BX are
- BD=21cmandBX=5.4cm.
- BD=15cmandBX=9.6cm.
- BD=25cmandBX=5.5cm.
- BD=9.6cmandBX=15cm.
Q.
If a quadrilateral ABCD is drawn to circumscribe a circle, then which of the options is true?
AB + CD = BC + AD
AC + AD = BD + CD
AC + AD = BC + DB
AB + CD = AC + BC
Q.
A quadrilateral ABCD is drawn to circumscribe a circle. Pair the equal sides.
![](https://search-static.byjusweb.com/question-images/byjus/ckeditor_assets/pictures/835687/original_91.png)
- AP
- CQ
- BP
- DR
- DS
- AS
- CR
- BQ
Q.
For the given quadrilateral, find BC + AD.
20 cm
15 cm
19 cm
14 cm