Locus of the Points Equidistant From Two Concentric Circles

Q. If radii of two consecutive circles are 15cm and 17cm then find the length of one circle which is tangent to one other

Q.

The locus of a point which is equidistant from two concentric circles is the ___ concentric with the given circles.

1. circle

2. triangle

3. line

4. parallel line

Q. If radii of the two concentric circles are 15 cm and 17 cm, then the length of each chord of one circle which is tangent to other is:

(a) 8 cm

(b) 16 cm

(c) 30 cm

(d) 17 cm

Q. In the given figure, O is the centre of a circle, BOA is its diameter and the tangent at the point P meets BA extended at T. If ∠PBO = 30^∘ then ∠PTA = ?
(a) 60^∘
(b) 30^∘
(c) 15^∘
(d) 45^∘

Q.

Describe the locus for questions 1 to 13 given below:

The locus of the centres of all circles passing through two fixed points.

Q. At one end A of a diameter AB of a circle of radius 5 cm , tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is
(a) 4 cm (b) 5 cm (c) 6 cm (d) 8 cm

Q.

Consider the circle which is named 'A' and has a radius of 7 cm. Then the locus of a point which is at a distance of 3 cm from this circle is/are the concentric circle(s)

1. C and D

2. B and D

3. B

4. B and C

Q. Locus of a point which is at a distance of 2 cm from a circle of radius 8 cm are the concentric circles of radii .

1. 5 cm and 11 cm
2. 4 cm and 12 cm
3. 6 cm and 10 cm
4. 7 cm and 9 cm

Q.

Describe:

(i) The locus of points at distances less than 3 cm from a given point.

(ii) The locus of points at distances greater than 4 cm from a given point.

(iii) The locus of points at distances less than 2.5 cm from a given point.

(iv) The locus of points at distances greater than or equal to 35 mm cm from a given point.

(v) The locus of the centre of a given circle which rolls around the outside of a second circle and is always touching it.

(vi) The locus of the centres of all circles that are tangent to both the arms of a given angle.

(vii) The locus of the mid-points of all chords parallel to a given chord of a circle.

(viii) The locus of points within a circle that are equidistant from the end points of a given chord.

Q.

Describe the locus for questions 1 to 13 given below:

The locus of a runner running around a circular track and always keeping a distance of 1.5 m from the inner edge.

Q. The locus of a point equidistant from two concentric circles is

1. Square
2. Triangle
3. Circle
4. Rhombus

Q. In the given figure, O is the centre of the circle. PA and PB. Show that AOBP is a cyclic quadrilateral [CBSE 2014]

Q. Locus of a point which is equidistant from two concentric circles is the circle concentric with the given circles and midway between them.

1. True
2. False

Q. O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then, the area of quadrilateral PQOR is


(a) 60 cm²
(b) 32.5 cm²
(c) 65 cm²
(d) 30 cm²