Circles Important Questions Prove that the lengths of tangents drawn from an external point to a circle are equal. Read More » Prove that the tangents drawn at the end points of a chord of a circle makes equal Read More » A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs Read More » In the given figure, a circle centered at origin O has radius 7 cm, OC is median of ΔOAB. Read More » In the given figure, AB and CD are tangents to a circle centred at O. Is angle BAC = angle DCA ? Read More » In the given figure, PQ is tangent to a circle centred at O and ∠BAQ = 30°; show that BP = BQ. Read More » In the given figure, AB, BC, CD and DA are tangents to the circle with centre O forming a quadrilateral Read More » The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector. Read More » A circle is touching the side BC of a A ABC at the point P and touching AB Read More » Find the area of the minor and the major sectors of a circle with radius 6 cm, Read More » If a chord of a circle of radius 10 cm subtends an angle of 60 deg at the centre Read More » In a park, four poles are standing at positions A, B, C and D around the circular fountain Read More » The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector. Read More » In the given figure, diameters AC and BD of the circle intersect at O. If ∠AOB = 60° and OA = 10 cm, then Read More » In the given figure, AB is a diameter of the circle with centre O. AQ, BP and Read More » A circle with centre O and radius 8 cm is inscribed in a quadrilateral ABCD in which P, Q, R, S are the points Read More » A backyard is in the shape of a triangle ABC with right angle at B. Read More » If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA. Read More » A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners Read More » A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and Read More » An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find: (i) the length Read More » Pookalam is the flower bed or flower pattern designed during Onam in Kerala. Read More » In figure 1, a right triangle ABC in which ∠B = 90 is shown. Taking AB as diameter, a circle has been drawn Read More » PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are Read More » Find upto three places of decimal the radius of the circle whose area is the sum of the areas of two Read More » In the given figure, ABC is a triangle in which ∠B = 90, BC = 48 cm and AB = 14 cm. Read More » A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the figure. Prove that AB + CD = AD + BC Read More » In the given figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30 . Read More » Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in Read More » If a, b and c are the sides of a right angled triangle, where c is hypotenuse, Read More » In figure, PQ is a tangent from an external point P to a circle with centre O Read More » A pendulum swings through an angle of 30 degree and describes an arc of 8.8 cm in length. Read More » A horse is placed for grazing inside a rectangular field 70 m by 52 m and is tethered to one corner Read More » Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Read More » In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P. Read More » PA and PB are tangents drawn to a circle of centre O from an external point P. Chord AB makes and Read More » Find the area of the unshaded region shown in the given figure. Read More » With vertices A, B and C of Δ ABC as centres, arcs are drawn with radii 14 cm and the three portions Read More » From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At a point E Read More » A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a Read More » Two circles with centres O and O’ of radii 6 cm and 8 cm, respectively intersect at two Read More » A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and Read More » In the given figure, PT is the tangent to the circle centered at O. OC is Perpendicular to Read More » Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle Read More » Two concentric circle are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. Read More » Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle Read More » In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that ∠ QAP + ∠ APR = 90°. Read More » A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Read More » In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If ∠ BAC = 65°, then find the measure of ∠ BOC. Read More » The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise Read More » In the given figure, a circle is inscribed in a quadrilateral ABCD in which ∠B = 900. If AD = 17 cm, AB = 20 cm and DS = 3 cm, then find the radius of the circle Read More » Two tangents TP and TQ are drawn to a circle with centre 0 from an external point T. Prove that ∠PTQ = 2∠OPQ Read More »

In the given figure, a circle centered at origin O has radius 7 cm, OC is median of ΔOAB. Read More »

In the given figure, AB and CD are tangents to a circle centred at O. Is angle BAC = angle DCA ? Read More »

In the given figure, PQ is tangent to a circle centred at O and ∠BAQ = 30°; show that BP = BQ. Read More »

In the given figure, AB, BC, CD and DA are tangents to the circle with centre O forming a quadrilateral Read More »

The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector. Read More »

In a park, four poles are standing at positions A, B, C and D around the circular fountain Read More »

The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector. Read More »

In the given figure, diameters AC and BD of the circle intersect at O. If ∠AOB = 60° and OA = 10 cm, then Read More »

A circle with centre O and radius 8 cm is inscribed in a quadrilateral ABCD in which P, Q, R, S are the points Read More »

A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and Read More »

An arc of a circle of radius 21 cm subtends an angle of 60° at the centre. Find: (i) the length Read More »

In figure 1, a right triangle ABC in which ∠B = 90 is shown. Taking AB as diameter, a circle has been drawn Read More »

PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are Read More »

Find upto three places of decimal the radius of the circle whose area is the sum of the areas of two Read More »

A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the figure. Prove that AB + CD = AD + BC Read More »

Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in Read More »

A pendulum swings through an angle of 30 degree and describes an arc of 8.8 cm in length. Read More »

A horse is placed for grazing inside a rectangular field 70 m by 52 m and is tethered to one corner Read More »

In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P. Read More »

PA and PB are tangents drawn to a circle of centre O from an external point P. Chord AB makes and Read More »

With vertices A, B and C of Δ ABC as centres, arcs are drawn with radii 14 cm and the three portions Read More »

From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At a point E Read More »

A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a Read More »

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and Read More »

In the given figure, PT is the tangent to the circle centered at O. OC is Perpendicular to Read More »

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle Read More »

Two concentric circle are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. Read More »

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle Read More »

In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that ∠ QAP + ∠ APR = 90°. Read More »

A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Read More »

In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If ∠ BAC = 65°, then find the measure of ∠ BOC. Read More »

The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise Read More »

In the given figure, a circle is inscribed in a quadrilateral ABCD in which ∠B = 900. If AD = 17 cm, AB = 20 cm and DS = 3 cm, then find the radius of the circle Read More »

Two tangents TP and TQ are drawn to a circle with centre 0 from an external point T. Prove that ∠PTQ = 2∠OPQ Read More »