Circles

Two circles C₁ and C₂ touch each other externally. The radius of C₁ is 16 cm and the radius of C₂ is 8 cm. Find the leng...

A, B, and C are three points such that $AB = 9 \text{ cm}$, $BC = 11 \text{ cm}$, and $AC = 20 \text{ cm}$. The number o...

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

Let C be a circle with centre O and P be an external point to C. Let PA and PB be two tangents to C with A and B being t...

From a circle with a radius of 15.75 cm, a sector with an arc length of 11 cm is cut off. Find the area (in cm²) of this...

In the figure, quadrilateral PQRS has its vertices on the circumference of the circle with centre O. If the measure of a...

From a point T, a tangent TP at point P is drawn to a circle with centre O. A secant TQR (point Q is near to point T) is...

In a circle with center O, an arc ABC subtends an angle of 138° at the centre of the circle. The chord AB is produced to...

A secant PAB is drawn from an external point P to the circle with the centre at O, intersecting it at A and B. If OP = 1...

The ratio of circumference and diameter of a circle is $3 : 5$. If the circumference is $6 \text{ cm}$, then the radius ...

From a point T, the length of the tangent to a circle is 32 cm and the distance of T from the centre is 40 cm. Find the ...

The radius of the circle is 8 cm. The distance of a point lying outside the circle from the centre is 17 cm. Find the le...

AB and CD are two parallel chords drawn in a circle with centre O. The distance between the two chords is 21 cm. If the ...

P and Q are centres of two circles whose radii are 7 cm and 3 cm, respectively. If the direct common tangents to the cir...

From a point A, which is at a distance of 17 cm from the centre C of a circle with radius 8 cm, the pair of tangents AB ...

A quadrilateral PQRS is inscribed in a circle of centre O, such that PQ is a diameter and ∠PSR = 120°. Find the value of...

AB is a chord of length 32 cm of a circle of radius 20 cm. The tangents at points A and B intersect at point T. Find the...

In a circle with centre $O$, an arc $ABC$ subtends an angle of $134^ ext{o}$ at the centre of the circle. The chord $AB$...

Akshay places three identical rings of diameter $21 \text{ cm}$ such that each ring touches the other two. Find the area...

The ratio of circumference and diameter of a circle is 3 : 5. If the circumference is 6 cm, then what is the radius of t...

R is a point outside a circle and is 18 cm away from its centre. A secant drawn from the point R intersects the circle a...

On a circle of radius 7 units, PQ and QR are chords of length 7 units each. What is the length of the chord PR in units?...

In a circle with centre O, AOC is the diameter. B is a point on the circumference of the circle such that arc AB is 1/5 ...

A circular arc whose radius is 14 cm makes an angle of 45° at the centre. Find the perimeter (in cm) of the sector. (Use...

The two circles intersect at two points P and Q. PR and PS are diameters of the two circles. What is ∠PQR ?...

Find the diameter (in cm) of a circle whose circumference is equal to the sum of the circumferences of two circles of ra...

The centres of two circles are 36 cm apart. If the radii of these two circles are 15 cm and 9 cm, respectively, then wha...

It is always possible to draw a circle passing through ______ non-collinear points in a plane....

M and N are the centres of two circles with radii 12 cm and 8 cm respectively. QR is the common tangent to the circles. ...

Two circles, centred at P and Q, intersect at two points C and D. AB is tangent to the two circles at A and B. If ∠ADB =...

Let C be a circle with centre O and PQ be a minor arc on C. Let R and S be two points on the major arc of PQ on C. If PQ...

The radii of two circles are 8 cm and 15 cm. Find the perimeter of the circle having area equal to the sum of the areas ...

The radii of two concentric circles are 26 cm and 10 cm. If a chord of the greater circle is tangent to the smaller circ...

A chord of the larger among two concentric circles is of length 20 cm and it is tangent to the smaller circle. What is t...

From a circle of radius 7 units, an arc length is cut by a chord of length 7 units. What is the arc length of the smalle...

A and B are centres of two circles with radii 2 cm and 1 cm respectively, where AB = 5 cm. C is the centre of another ci...

PQ is the diameter of a circle with centre A. M is a point on the circumference of the circle. If the measure of angle M...

The radius of a circle is 12.5 cm and the length of one of its chords is 11 cm. What is the distance of the chord from t...

A pair of straight lines from an external point F intersects a circle at A and B (FA < FB), and touches the circle at C....

Two circles of radii 18 cm and 12 cm touch each other externally. Find the length (in cm) of their direct common tangent...

What is the central angle (in degrees, rounded up to one decimal place) of a sector of a circle whose area and perimeter...

If the length of a common external tangent to two circles is 9 and that of a common internal tangent is 5, then what is ...

XAB and XCD are two secants to a circle. If XA = 18 cm, AB = 22 cm and XC = 24 cm, then find the value of XD (in cm)....

AB is the chord of the circle with centre O. A line segment DOC originating from a point D on the circumference of the c...

The distance between the longest chord and the centre of a circle is:...

Find the area (in cm²) of the sector whose perimeter is 64/3 cm and central angle is 60°. Use π = 22/7....

If in a circle a chord of length 14 cm is at a distance of 24 cm from its centre, then the length of the radius of the c...

The length of the tangent drawn from a point 10 cm away from the centre of a circle with radius 4 cm is:...

At what angle is the arc length half the perimeter of the circle?...

If the area of a sector of a circle is 462 cm² and the central angle is 120°, then what is the radius of the circle?...