A,B, C are three points such that AB = 9 cm, BC = 11 cm and AC = 20 cm. The number of circles passing through points A,B,C is:

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?

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

One chord of a circle is given as 20.5 cm. Then the radius (r) of the circle must be:

If the radii of two circles are 6 cm and 3 cm and the length of the transverse common tangent is 8 cm, then the distance between the two circles is:

Two circles of radius 7 units each, intersect in such a way that the common chord is of length 7 units. What is the common area in square units of the intersection?

The radius of a circle is 10 cm. The angle made by chord AB at the center of this circle is 60 degrees. What is the length of this chord?

Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is \(5\sqrt{13}\)cm. What is the distance between the chords?

The length of the tangent to a circle from a point P is 15 cm. Point P is 17 cm away from the centre. What is the radius of the circle?

CD is a tangent to a circle of circumference of 88 cm with its centre at O. OC cuts the circle at P while OD cuts circle at V such that ∠COD = 90°. Length of PC is 6 cm. What is half of CD (in cm) if OD exceeds OC by 1 cm?

What is the length of the chord formed by on the line y = 1 in the circle (x – 1)² + (y – 1)² = 4?

The number of parallel tangents of a circle with a given tangent is:

A chord of length 40 cm is drawn in a circle having a diameter of 50 cm. What is the minimum distance of the other parallel chord of length 30 cm in the same circle from the 40 cm long chord?

How many circles can be drawn that pass through two fixed points?

Two circles with centers P and Q of radii 6 cm and 4 cm, respectively, touch each other internally. If the perpendicular bisector of PQ meets the bigger circle in A and B, then the value of AB is:

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.

Two circles of radius 12 cm and 15 cm intersect each other at points A and B. If the length of the common chord is 12 cm, then what is the distance between their centres?

In a circle centered at O, PQ is a tangent at P. Furthermore, AB is the chord of the circle and is extended to Q. If PQ = 12 cm and QB = 8 cm, then the length of AB is equal to:

The length of the common chord of two intersecting circles is 24 cm. If the diameter of the circles is 30 cm and 26 cm, then the distance between the centers (in cm) is:

AB is a chord of a circle having a radius 1.7 cm. If the distance of this chord AB from the center of the circle is 0.8 cm, then what is the length (in cm) of the chord AB?

In two circles centered at O and O’, the distance between the centres of both circles is 17 cm. The points of contact of a direct common tangent between the circles are P and Q. If the radii of both circles are 7 cm and 15 cm, respectively, then the length of PQ is equal to:

In a circle, chords AB and CD intersect internally at E. If CD = 18 cm, DE = 5cm, AE = 13 cm, then the length of BE 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?

The length of tangent from the point (5, 1) to the circle x² + y² + 6x - 4y - 3 = 0, is

A tangent is drawn from point M to a circle, which meets the circle at T such that MT= 12 cm. A secant MAB intersects the circle at points A and B. If MA = 8 cm, what is the length (in cm) of the chord AB?

Out of two concentric circles, the radius of the outer circle is 6 cm and the chord PQ of the length 10 cm is a tangent to the inner circle. Find the radius (in cm) of the inner circle.

Let O be the centre of a circle and P be the point outside the circle. If PAB is a secant to the circle intersecting the circle at A and B and PT is the tangent segment drawn from P, find the length of PT, if PA = 3 cm and AB = 9 cm.

Let C be a circle with a center O and a radius 5 cm. Let PQ be a tangent to the circle and A be the point of tangency. Let B be a point on PQ such that the length of AB is 12 cm. If the line joining O and B intersects the circle at R, find the length of BR (in cm).

AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. If the distance between them is 2 cm, then the radius (in cm) of the circle is:

A circle has a radius of 5 cm and the length of tangent drawn from a point X outside the circle is 12 cm. The distance of the point x from the centre of the circle is:

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:

If the distance between the centers of two circles is 12 cm and the radii are 5 cm and 4 cm, then the length (in cm) of the transverse common tangent is:

In a circle with a radius of 20 cm, X is a point located at a distance of 29 cm from the center of the circle. What will be the length (in cm) of a tangent drawn from point X to the circle?

Two circles touch each other externally, having a radius of 12 cm and 8 cm, respectively. Find the length of their common tangent, AB with point A on the bigger circle and B on the smaller circle.

A tangent at point A of a circle of radius 6 cm meets a line through the centre O at point B. If OB = 10 cm, then the length of AB (in cm) is equal to:

AD is a tangent of a circle, and ABC is the secant. If AB = 8 cm and BC = 10 cm, then find the length of AD.

A circle with a center O has a chord AB that is 20 cm in length. If the radius of the circle is 12 cm, then the area of triangle AOB is:

What is the length of the chord formed by on the line y = 1 in the circle (x – 1)² + (y – 1)² = 4?

The distance between the centers of two circles having radii of 24 cm and 18 cm, respectively, is 48 cm. Find the length (in cm) of a direct common tangent to the two circles.

The radius of a circle is 3 cm and 'O' is its centre. The length of the tangent (in cm) to the circle drawn from a point P, which is at a distance of 5 cm from 'O' is:

A direct common tangent is drawn to two circles of radius 25cm and 20 cm. The centers of the two circles are 35 cm apart. What is the length (in cm) of the tangent?

If the area of the circle is 616 cm² and a chord XY = 10 then find the perpendicular distance from the center of the circle to the chord XY.

Two concentric circles of radii 15 cm and 13 cm are given. Find the length of the chord of the larger circle which touches the smaller circle.

Which of the following statements is INCORRECT?

A 15-cm-long perpendicular is drawn from the center of a circle to its 40-cm-long chord. Find the radius of the circle.

Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Two circles of radii 10 cm and 5 cm touch each other externally at point A. PQ is the direct common tangent of those two circles of centers O₁ and O₂ respectively. The length of PQ is equal to:

The distance between the centres of two circles having radii 16 cm and 8 cm, is 26 cm. The length (in cm) of the direct common tangent of the two circles is:

In a circle, a 14 cm long chord is at 24 cm from the centre of the circle. Find the length of the radius of the circle.

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.