Perpendicular from the Center to a Chord Bisects the Chord

Q. The length of a chord of a circle of 16.8 cm, radius is 9.1 cm. Find its distance from the centre.

Q. C is the centre of the circle whose radius is 10 cm. Find the distance of the chord from the centre if the length of the chord is 12 cm.

1. 6 cm
2. 7 cm
3. 8 cm
4. 9 cm

Q. A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance 'a'. Find the distance of the foot of the ladder from the wall.

1. 3m
2. 6m
3. 9m
4. 12m

Q. The area of a trapezium is 400 cm${}^2$, the distance between the parallel sides is 16 cm. If one of the parallel sides is 20 cm, find the length of the other side.

Q. Find the area of the trapezium whose parallel sides are 12m and 20m respectively and distance between them is 10m.

Q.

A circle of radius 3 cm, with centre O is drawn circumscribing a $\Delta$ABC. What is the sum of OA + OB + OC ?

1. 3 cm

2. 6 cm

3. 9 cm

4. 12 cm

Q.

PQ and RS are two parallel chords of a circle whose centre is O and radius is 5 cm. If PQ = 8 cm and RS = 6 cm.What is the distance between PQ and RS if they lie on the same side of the centre?

1. 1cm
2. 2cm
3. 3cm
4. 4cm

Q.

Question 19

The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is

$\left(a\right)124c{m}^2$
$\left(b\right)118c{m}^2$
$\left(c\right)128c{m}^2$
$\left(d\right)112c{m}^2$

Q.

The outer wheel of a ferris wheel is made of several steel arcs. If two arcs of equal length AB and PQ are taken, and the chord forming arc AB is measured to be 60 cm. What would be the length of chord forming arc PQ?

1. 120 cm
2. 40 cm
3. 60 cm
4. 30 cm

Q. A $2.0$ g sample containing ${Na}_{2}C{O}_3$ and $NaHC{O}_3$ loses $0.248$ g when heated to $300$${}^{o}C$, the temperature at which $NaHC{O}_3$ decomposes to ${Na}_{2}C{O}_3,C{O}_2$ and $H_{2}O$. The $\%$ of ${Na}_{2}C{O}_3$ in the mixture is (as the nearest integer):

Q. In a circle with center O, a perpendicular is dropped from the center to a chord RT. Find the length of RO, if length of RT = 12 cm and QO = 8 cm.

1. 10 cm
2. 7 cm
3. 11 cm
4. 14 cm

Q. In the given figure, AB is the chord to the circle having centre at O. If AC = CB and $\angle AOC={50}^{\circ }$, then find $\angle CAO$.

1. ${30}^{\circ }$
2. ${50}^{\circ }$
3. ${40}^{\circ }$
4. ${50}^{\circ }$

Q.

The figure given below, shows a circle with centre O in which diameter AB bisects the chord CD perpendicularly at point E . If CD =16 cm & EB = 4 cm. find the radius of the circle.

1. 10 cm

2. 11 cm

3. 8 cm

4. 6 cm

Q. The shortest distance of point A from line l is _____

1. AB
2. AC
3. AD
4. AE

Q.

PQ and RS are two parallel chords of a circle whose centre is O and radius is 5 cm. If PQ = 8 cm and RS = 6 cm.The distance between PQ and RS if they lie on the same side of the centre is ___ cm

Q. In a circle with center O, a perpendicular is dropped from the center to a chord AB. Find the length of AO, if length of AB = 8 cm and CO = 3 cm.

1. 2 cm
2. 3.5 cm
3. 5 cm
4. 6 cm

Q. The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is

Q.

A circle with center O and Diameter equal to 26 cm has a chord AB on it. OM perpendicular to AB has length equal to 5 cm. Find the length of the chord.

1. 11 cm.

2. 9 cm

3. 12 cm

Q.

A circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, the radius of the circle is

1. 16 cm

2. 20 cm

3. 10 cm

4. 8.5 cm

Q. In Fig. 3, if O is the centre of the circle ; OL$=$4 cm, AB $=$6 cm and OM$=$ 3 cm, then CD$=$?

1. 6cm
2. 4cm
3. 8cm
4. 10cm

Q. Height of trapezium if half the sum of parallel sides which are 13 cm and 25 cm. Find its area.

1. 361 cm^2
2. 360 cm^2
3. 300 cm^2
4. 261 cm^2

Q. Area of a trapezium = $2h\times (a+b)$
where h is the distance between the parallel sides a and b.

1. False
2. True

Q. The area of a trapezium is 256 sq cm. If the lengths of its parallel sides are 7 cm and 9 cm, find its height.

1. 32 cm
2. 8 cm
3. 48 cm
4. 16 cm

Q. Area of a trapezium = $2h\times (a+b)$
where h is the distance between the parallel sides a and b.

1. True
2. False

Q. Area of a trapezium = $2h\times (a+b)$
where h is the distance between the parallel sides a and b.

1. True
2. False

Q. Find the distance of a perpendicular from the centre of a circle to the chord if the diameter of the circle is $30cm$ and its chord is $24cm.$

1. $6cm$
2. $7cm$
3. $9cm$
4. $10cm$

Q. Solve:
$\frac{x}{x+1}+\frac{x+1}{x}=\frac{5}{2}$

Q. Area of a trapezium = $2h\times (a+b)$
where h is the distance between the parallel sides a and b.

1. True
2. False