Converse of Theorem 4

Q. A quadrilateral becomes parallelogram, if its diagonal intersect in the ratio______

1. 1:2
2. 2:1
3. 1:1
4. 3:2

Q.

XY and PQ are two parallel chords of a circle on opposite side of the centre O and radius of circle is 13 cm. if PQ = 10 cm and XY = 24 cm, find the distance between PQ and XY.

1. 17 cm

2. 14 cm

3. 21 cm

4. 25 cm

Q.

A quadrilateral can be divided into two congruent triangles. If the opposite sides are non-parallel, the quadrilateral is called ___.

1. Rhombus

2. Square

3. Kite

4. Rectangle

Q. Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?

Q. In a circle with radius 13 cm, two equal chords are at a distance of 5 cm from the centre. Find the lengths of the chords.

Q. In the given figure AB and CD are two chords of a circle having centre at O.Two perpendicular lines OE and OF are having equal lenghs are drawn as shown.If AB = 10 cm , then the length of CD is equal to

1. 5 cm
2. 7.5 cm
3. 10 cm
4. 15 cm

Q.

The diagonals of the rectangle are not congruent.

1. True
2. False

Q. 50. If each diagonal of a quadrilateral divides it into two triangles of equal area , then prove that the quadrilateral is a parallelogram.

Q. A quadrilateral can be divided into two congruent triangles. If the opposite sides are non-parallel, the quadrilateral is called

1. Rectangle
2. Kite
3. Rhombus

Q.

AB and PQ are two equal chords of a circle. If the length of minor arc and major arc formed by AB is 24cm and 64cm respectively, then the length of minor and major arc formed by PQ is ___ and ___ respectively.

1. 24 cm, 64 cm

2. 64 cm, 24 cm

3. 12 cm, 32 cm

4. 32 cm, 12 cm

Q. In the given figure AB and CD are two chord of a circle having centre at O.Two perpendicular line OE and OF having equal lenghs are drawn as shown.If AB = 12 cm , then the length of FD is equal to__.

1. 6 cm
2. 18 cm
3. 12 cm
4. 24 cm

Q. Two chords AB and CD of lengths 5cm and 11cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6cm, find the radius of that circle.

Q.

Two circles of radii10 cm and 8 cm intersect and the length of the common chord is 12 cm. The distance between their centres is

1. 6 cm

2. 3 cm

3. 8 cm

4. 5 cm

Q.

During maths lab activity, teacher gives four sticks of lengths 6 cm, 6 cm, 4 cm and 4 cm to each student to make different types of quadrilateral.

She asks following questions from the students:
Q. A diagonal of a parallelogram divides it into two _______ triangles.

1. Equilateral
2. Similar
3. Congruent
4. Right angled

Q. Prove that equal chords of a circle are equidistant from the centre.

Q. AB and CD are two chords of a circle on the same side of the center such that AB = 8 cm, CD = 10 cm and AB|| CD. If the distance between AB and CD is 2 cm, then find the radius of the circle.

Q. The diagonals of a Quadrilateral divide it into four congruent triangles. The Quadrilateral is a _____________.

1. Parallelogram
2. Rectangle
3. Rhombus
4. None of the above

Q. In the given figure, if AB=10 cm, then CD= ____.

1. 10 cm
2. 7.5 cm
3. 5 cm
4. 2.5 cm

Q. Two chords PQ and PR of a circle are equal then prove that the bisector of $\angle$RPQ passes through the centre of the circle.

Q.

For the given figure, find the relation between the chords, $AB$ and $CD$.

1. $AB=\frac{1}{a}CD$

2. $AB=2CD$

3. $AB=a.CD$

4. $AB=CD$

Q.

Chords AB and CD of a circle with centre O, intersect at a point E. If OE bisects $\angle$AED, then chord AB = CD.

1. 60°

2. 45°

Q. PQRS is a parallleogram, then PR ___ QS

1. perpendicular
2. parallel
3. bisects
4. not equal to

Q.
Identify the correct relations with respect to the given parallelogram.

1. ∠1 = ∠4
2. ∠1 = ∠5
3. ∠6 = ∠5
4. ∠6 = ∠2
5. ∠1 = ∠2
6. ∠4 = ∠3
7. DO = OB
8. AO = OC
9. AB = DC
10. AD = BC

Q. Prove that congruent chords of a circle are equidistant from the centers.

Q. In the given figure, AB and AC are two equal chords of a circle with centre O. Show that O lies on the bisectors of ∠BAC.

Q. If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.

Q. In the given diagram, AD is a diameter of the circle and AB is a chord. If AO= 17 cm, AB = 30 cm, the distance of AB from the centre of the circle is

1. 17 cm
2. 15 cm
3. 8 cm
4. 4 cm

Q.
Identify the correct relations with respect to the given parallelogram.

1. ∠1 = ∠4
2. ∠1 = ∠5
3. ∠6 = ∠5
4. ∠6 = ∠2
5. ∠1 = ∠2
6. ∠4 = ∠3
7. DO = OB
8. AO = OC
9. AB = DC
10. AD = BC

Q. AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, then the radius of the circle is _____.

1. 14 cm
2. 10 cm
3. 13 cm
4. 15 cm

Q.

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?