Mathematics exemplar problems class 10 Solutions for Chapter 9 circles

In Fig, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, then ∠BAT is equal to

If radii of two concentric circles are 4 cm and 5 cm, then the length of chord of one circle which is tangent to the other circle is

In the given figure, AT is a tangent to the circle with centre ‘O’ such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to

In the given figure, ‘O’ is the centre of circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to

In the given figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, then ∠OAB is equal to

If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then the length of each tangent is equal to

In the given figure, if PQR is the tangent to a circle at Q, whose centre is O, AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to

From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is

If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then OP = a√3.

If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.

The length of tangent from an external point P on a circle with centre O is always less than OP.

The tangent to the circumcircle of an isosceles ΔABC at A, in which AB = AC, is parallel to BC.

If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then OP = a√2.

AB is a diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersects AB extended at D, then BC = BD.

The angle between two tangents to a circle may be 0°.

The length of tangent from an external point on a circle is always greater than the radius of the circle.

If a number of circles touch a given line segment PQ at as point A, then their centre lies on the perpendicular bisector of PQ.

If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.

If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that angle DBC = 120°, state whether BO = 2BC.

In figure, AB and CD are common tangents to two circles of unequal radii. State whether AB = CD.

If radii of the two circles are equal, check if AB = CD.

In the given figure, common tangent AB and CD to two circles intersect at E. State whether AB = CD.

Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle.

Two tangents PQ and PR are drawn from an external point to a circle with centre O. State whether QORP is a cyclic quadrilateral.

Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, state whether BD = s – b.

If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in Figure. State whether ∠BAT = ∠ACB

In figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find the ∠RQS.

AB is a diameter and AC is chord of a circle with centre O such that ∠BAC = 30°. The tangent at C intersects extended AB at a point D. State whether BC = BD.

If an isosceles ΔABC in which AB = AC = 6 cm is inscribed in a circle of radius 9 cm, find the area of the triangle.

A is a point at a distance 13 cm from the centre ‘O’ of a circle of radius 5 cm. AP and AQ are the tangents to circle at P and Q. If a tangent BC is drawn at point R lying on minor arc PQ to intersect AP at B and AQ at C. Find the perimeter of ΔABC.

Two circles with centres O and O’ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ.

From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

In the given figure, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB.

If a hexagon ABCDEF circumscribe a circle, state whether AB + CD + EF = BC + DE + FA.

The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA = 110°, find ∠CBA.

Assertion: In the given figure, if PQ is a tangent to the circle with center O, then the value of ∠POQ is 25°.

Reason: If two tangents are drawn to a circle from an external point, then they subtend equal angles at the center.

Choose the correct option based on the assertion and reason given above.