Two circles of the same radius 6 cm, intersect each other at P and Q. If PQ = 10cm, then what is the distance between the centers of the two circles?

The distance between the centres of two circles of radii 2cm and 6 cm is 5 cm. Find the length of the direct common tangent.

From a point Q, the length of the tangent to a circle is 20 cm and the distance of Q from the centre of the circle is 25 cm. The radius of the circle is:

In the given figure, the diameter AB and chord CD of a circle meet at P. PT is tangent to the circle at T. If CD = 8 cm, PD = 10 cm, and PB = 8 cm, find AB.

Two chords of a circle AB and CD meet at a point P outside the circle. If AP = 200 mm, AB = 120 mm, and CP =160 mm, then what is the length of CD?

A 15 cm long perpendicular is drawn from the centre of a circle to a 40-cm-long chord. Find the diameter of the circle.

PT is a tangent to a circle whose centre is O, and where T is a point on the circle. If PT = 12 cm and PO = 13 cm, then find the radius of the circle.

C1 and C2 are two concentric circles such that the radius of C2 is less than the radius of C1. If AB is the chord of C1 of length 12 cm, touching C2 at P, find the length of AP.

A chord is drawn inside the bigger circle of two concentric circles with radii of 25 cm and 15 cm respectively. If the chord to the outer circle is such that, it touches the smaller circle at exactly 1 point, find the length of the chord.

If the length of a chord, drawn at a distance of 21 cm from the centre of a circle, is 40 cm, then the radius (in cm) of the circle is:

What is the length (in cm) of the transverse common tangent between two circles with radii 6 cm and 4 cm, given that the distance between their centres is 14 cm?

Two circles with centers B and O have radii OA = 8 cm and BC = x cm, respectively. AC is tangent to both circles. If OB and AC intersect the point E, AE = 12 cm and EC = 18 cm, then find the value of x (in cm).

In a circle of radius 8 units, a chord of length 10 units is drawn. What is the perpendicular distance of the chord from the centre of the circle in units?

Two circles of radius 6 cm each. They intersect each other such that each passes through the centre of the other. What is the length of the common chord?

AB is the common tangent to both circles as shown in the given figure. What is the distance between the centres of the circles?

In a cyclic quadrilateral PQRS, SR and PQ are extended to meet at point T. If TS = 16 cm, TR = 12 cm and TQ = 8 cm, then the length of the TP in cm is?

Two tangents PR and PT are drawn on a circle of radius 'r' where PQ = 16 m and PS = 10 m then what would be the radius of the circle?

AB is a chord in a circle having a radius of 29 cm. PQ is another chord in the same circle. If the length of AB is 42 cm and the length of PQ is 40 cm, then find the maximum possible perpendicular distance between AB and PQ.

Two circles of equal radii of 6 cm intersect each other such that each circle passes through the centre of the other circle. Find the length of the chord that is common to both the circles.

A tangent drawn from an external point ‘P’ meets a circle at point ‘Q’. If ‘O’ is the centre of the circle with a radius of 8 cm, and PQ = x cm and PO = (x + 2) cm, then find the value of ‘x’.

Chords AB and CD of a circle, when produced, meet at a point P outside the circle, If AB = 8 cm, BP = 4 cm and CD = 2 cm then find the value of DP.

A circle with center O and two chords PQ and RS. Both the chords are parallel to each other on opposite sides of the center and the distance between the chords is 86 cm. The length of chord PQ is 122 cm and the length of chord RS is 118 cm. Then find the radius of the circle.

What is the length (in cm) of chord PQ in a circle with a radius of 7 cm, where a diameter AB and non-diameter chord PQ intersect perpendicularly at point C, and the ratio of AC to BC is 4 : 3?

In the given figure, MP is tangent to a circle with center A and NQ is a tangent to a circle with center B. If MP = 15 cm, NQ = 8 cm, PA = 17 cm and BQ = 10 cm, then AB is:

Two circles, each of radius 36 cm, intersect each other such that each circle passes through the centre of the other circle. What is the length of the common chord to the two circles?

Two circles touch each other externally as shown in the figure . The radius of the circle with centre O is 49 cm. The radius of the circle with centre A is 16 cm. Find the length (in cm) of their common tangent BC.

The radii of two concentric circles are x cm and 26 cm. P and S are the points on a larger circle, and Q and R are points on a smaller circle. If PQRS is a straight line and QR = 40 cm and PS = 48 cm, then what is the value of x? (x < 26 cm)

Two parallel chords are drawn in a circle of radius 25 cm. The distance between the two chords is 27 cm. If the length of one chord is 48 cm, then the length of the other chord is equal to:

A transverse common tangent is drawn to two circles of radius 8.5 cm and 5.5 cm. The centres of the two circles are 18 cm apart. What is the length (in cm) of the tangent?

Two circles of radius 2.4 cm and 4 cm, respectively, have a common tangent. The distance between the centres of the two circles is 6.5 cm. If the common tangent does not intersect the line joining the centers, then find the length of a common tangent to the circles.

Length of chord MN is 40 cm. The distance of the chord MN from the centre is 15 cm. What will be the radius of this circle?

If AB is a chord of a circle with a radius of 5 units and C is a point on the circle such that ∠ACB = \(\frac{\pi}{2}\), then the length of chord AB is:

O is the center of a circle with a diameter of 16 cm. Q is a point outside the circle and QS is tangent to the circle at point S. If OQ is = 17 cm, what is the length (in cm) of the tangent QS?

The length of the direct common tangent is 24 cm for two circles whose radii are 16 cm and 6 cm. What is the distance between their centres?

Two circles with diameters 50 cm and 58 cm, respectively, intersect each other at points A and B, such that the length of the common chord is 40 cm. Find the distance (in cm) between the centers of these two circles.

CT is a tangent to a circle at the point T on the circle. Chord AB of the circle is extended to meet the tangent CT at the point C. If m (AB) = 3 cm and m (BC) = 2.4 cm, find the length (in cm) of the tangent CT.

In the figure given below, two circles with centers O and P and radii 5 cm and 1 cm respectively meet internally. A chord AB of the bigger circle perpendicularly bisects OP, where OP is twice of OC. What is the length of AB? (in cm)

The lengths of two parallel chords of a circle are 10 cm and 24 cm lie on opposite sides of the centre. If the smaller chord is 12 cm from the centre, what is the distance (in cm) between the two chords?

Two points P and Q are 3 cm apart. These two points lle on the circumference of a circle having radius 1.7 cm. What is the distance (in cm) of the line segment PQ from the centre of the circle?

Two circles with centres A and B touch each externally, PQ is a direct common tangent which touches the circle at P and Q. If the radii of the circles are 9 cm and 4 cm, respectively, then the length of PQ (in cm) is equal to:

If the radii of two circles are 5√3 and 11√3 respectively and the distance between the centers of these circles is 48/√3. Find the number of common tangents that can be drawn to these circles.

If p and q are radii of two circles with centers L and M, then there will be ________ common tangents if \(|p - q| < LM < (p + q)\)?

Two circles with diameters 68 cm and 40 cm , intersect each other and the length of their common chord is 32 cm. find the distance between their centers?

In a circle with centre O, AB and CD are parallel chords on opposite sides of a diameter. If AB = 20 cm, CD = 28 cm, and the distance between the chords AB and CD is 16 cm, then find the radius of the circle (in cm).

In the given figure, AMD, APQ, and ASR are secants to the given circles. If AM = 6 cm, MD = 9 cm, and AS = 7.5 cm, then find the length of line segment SR.

If the radius of two circles be 6 cm and 9 cm and the length of the transverse common tangent be 20 cm , then find the distance between the two centres.

Chord AB of a circle with center O is produced to a point P, and C is a point on the circle such that PC is a tangent to the circle. If AB = 4.9 cm, BP = 6.3 cm, and OP = 14 cm then, find perimeter of circle:

Two mutually perpendicular chords AB and CD meet at a point P inside the circle such that AP = 6 cm, PB = 4 cm and DP = 3 cm. What is the area of the circle?

(i) What is the length of the common tangent XY?

Two circles of radii 12 cm and 13 cm are concentric. The length of the chord of the larger circle that touches the smaller circle is: