Sum of Opposite Sides Are Equal in a Quadrilateral Circumscribing a Circle

Q.

The parallelogram circumscribing a circle is a rhombus.

1. True

2. False

Q. The perimeter of the given quadrilateral ABCD circumscribing a circle is

1. 32 cm
2. 62 cm
3. 48 cm

Q.

If a quadrilateral ABCD is drawn to circumscribe a circle, then which of the options is true?

1. AC + AD = BD + CD

2. AB + CD = BC + AD

3. AC + AD = BC + DB

4. 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____.

1. AB+BC=CD+AD
2. AB-CD=BC-AD
3. AB+CD=BC+AD
4. 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.

1. 30 cm
2. 15 cm
3. 20 cm
4. 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

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.

Q. A circle is inscribed in a quadrilateral as shown below, then
AB + CD = BC + AD.

1. True
2. False

Q. A circle is inscribed in a quadrilateral as shown below, then
AB + CD = BC + AD.

1. True
2. False

Q. In a right-angled $\Delta ABC$ a circle with side $AB$ as diameter is drawn to intersect the hypotenuse $AC$in $L$. 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.

Q. If the sides of a quadrilateral ABCD touch a circle, then prove that AB+CD=BC+AD

Q. The perimeter of the given quadrilateral ABCD circumscribing a circle is

1. 32 cm
2. 62 cm
3. 48 cm

Q. A quadrilateral $ABCD$ is drawn to circumscribe a circle. Prove that $AB+CD=AD=BC$.

Q.

Solve the following:

In fig, quadrilateral ABCD is circumscribing a circle. Find the perimeter of the quadrilateral ABCD.

Q. Match the following:

1. AP + DR = 5 cm
2. DC = 7 cm
3. 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.

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

1. $BD=21cmandBX=5.4cm.$
2. $BD=15cmandBX=9.6cm.$
3. $BD=25cmandBX=5.5cm.$
4. $BD=9.6cmandBX=15cm.$

Q.

If a quadrilateral ABCD is drawn to circumscribe a circle, then which of the options is true?

1. AB + CD = BC + AD

2. AC + AD = BD + CD

3. AC + AD = BC + DB

4. AB + CD = AC + BC

Q. A quadrilateral ABCD is drawn to circumscribe a circle. Pair the equal sides.

1. AP
2. CQ
3. BP
4. DR
5. DS
6. AS
7. CR
8. BQ

Q.

For the given quadrilateral, find BC + AD.

1. 20 cm

2. 15 cm

3. 19 cm

4. 14 cm