# Chords Equidistant from Center Are Equal

## Trending Questions

**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.

10 cm

8 cm

12 cm

6 cm

**Q.**

Let ${S}_{1}={x}^{2}+{y}^{2}=9$ and ${S}_{2}={(x\u20132)}^{2}+{y}^{2}=1$. 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:

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

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

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

$(0,\pm \surd 3)$

**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 ∠PQR and ∠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 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of common chord.

5 cm

6 cm

7 cm

8 cm

**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.

24 cm

30 cm

38 cm

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

- 10 cm
- 13 cm
- 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=24 cm, ON=5 cm, OM=12 cm. Find the length of chord CD

**Q.**Calculate the length of a chord which is at a distance of 12 cm from the center of a circle of radius 13 cm

**Q.**Find the length of the chord joining the points in which the straight line xa+yb=1 meets the circle x2+y2=r2.

**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 5 cm from the centre of a circle of radius 13 cm.

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

- 17 cm
- 15 cm
- 4 cm
- 8 cm

**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=24 cm, OM=5 cm, ON=12 cm. Find the:

(i) radius of the circle.

(ii) length of chord CD.

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

**Q.**The radius of the circle is 10 cm and the length of one of its chords is 12 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 ∠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 ≅ 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 x2+y2−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.