Chords Equidistant from Center Are Equal

Q.

A chord of length 30 cm is drawn in a circle of radius 17 cm. Find its distance from the centre of the circle.

1. 10 cm

2. 8 cm

3. 12 cm

4. 6 cm

Q.

Let $S_1=x^2+y^2=9$ and $S_2={(x–2)}^2+y^2=1$. Then the locus of the Centre of a variable circle $S$ which touches $S_1$ internally and $S_2$ externally always passes through the points:

1. $\left(\frac{1}{2},\pm \frac{\sqrt{5}}{2}\right)$

2. $\left(2,\pm \frac{3}{2}\right)$

3. $\left(1,\pm 2\right)$

4. $(0,\pm \surd 3)$

Q.

PQ and RQ are chords of a circle equidistant from the centre and S is a point on the circle, such that QS forms diameter. Prove that the diameter QS bisects $\angle$PQR and $\angle$PSR.

Q. 29. Two equal chords AB and AC of the circle x^2+ y^2- 6x-8y -24= 0 are drawn from the point A(V33 +3, 0).Another chord PQ is drawn intersecting AB and AC at points R and S, respectively given that AR=SC =7 and RB =AS 3. The value of PR/QS is(a) 1(c) 2(d) None of these

Q.

Two circles of radii $5cm$ and $3cm$ intersect at two points and the distance between their centres is $4cm$. Find the length of common chord.

1. $5cm$

2. $6cm$

3. $7cm$

4. $8cm$

Q.

Chords AB & CD of a circle are parallel to each other and lie on opposite sides of the centre of the circle. If AB = 36 cm, CD = 48 cm and the distance between the chords is 42 cm. Find the radius of the circle.

1. 24 cm

2. 30 cm

3. 38 cm

4. 40 cm

Q. If two diameters of a circle intersect each other at right angles, then quadrilateral formed by joining their end points is a

(a) rhombus

(b) rectangle

(c) parallelogram

(d) square

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. AB and CD are parallel chords on opposite sides of centre of circle. If AB = 10 cm, CD = 24 cm, distance between chords is 17 cm, radius of circle is

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

Q. Two concentric circles are of radii $8cm$ and $5cm$.Find the length of the chords of the larger circle which touches the smaller circle.

Q. if O is the point of intersection of two chords AB and CD such that OB=OD and angle AOC=45 than triangles OAC and ODB ARE

Q. In the figure given, $O$ is the centre of the circle. $AB$ and $CD$ are two chords of the circle. $OM$ is perpendicular to $CD$ and $ON$ is perpendicular to $AB$. $AB=24cm,ON=5cm,OM=12cm$. Find the length of chord $CD$

Q. Calculate the length of a chord which is at a distance of $12\text{cm}$ from the center of a circle of radius $13\text{cm}$

Q. Find the length of the chord joining the points in which the straight line $\frac{x}{a}+\frac{y}{b}=1$ meets the circle $x^2+y^2=r^2$.

Q. Radius of a circle with centre $O$ is $41$ units. Length of a chord $P$ is $80$ units, find the distance of the chord from the centre of the circle.

Q. Find the length of a chord which is at a distance of $5cm$ from the centre of a circle of radius $13cm$.

Q. $AD$ is a diameter of a circle and $AB$ is a chord. If $AD=34cm,AB=30cm$, the distance of $AB$ from the centre of the circle is

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

Q. In the given figure, $O$ is the centre of the circle. $AB$ and $CD$ are two chords of the circle. $OM$ is perpendicular to $AB$ and $ON$ is perpendicular to $CD$. $AB=24cm,OM=5cm,ON=12cm$. Find the:
(i) radius of the circle.
(ii) length of chord $CD$.

Q. Two circles of radii $5cm$ and $3cm$ intersect at two points and the distance between their centres is $4cm$. Find the length of the common chord.

Q. The radius of the circle is $10\text{cm}$ and the length of one of its chords is $12\text{cm}$, then the distance of the chord from the center is

Q. The centre of a circle of radius 13 units is the point (3, 6). P(7, 9) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB.

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

Q. In a circle with centre O, diameter AD and diameter BC are given. Prove that chord AB $\cong$ chord CD.

Q. If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

Q. Find the length of the chord $x-y-3=0$ of the circle $x^2+y^2-x+3y-22=0$

Q.

If a line segment joining mid-points of two chords of a circle passes through the center of the circle, prove that the two chords are parallel?

Q. Radius of a circle with centre $O$ is $41$ units. Length of a chord $PQ$ is $80$ units, find the distance of the chord from the centre of the circle.

Q. 40. All chords through an external point to the circle x^2+y^2=16 are drawn having length I which is a positive integer. The sum of the squares of the distances fromcentre of circle to these chords is(a) 154 (b) 124 (c) 172 (d) 128

Q. Prove that Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).

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.