List of top Mathematics Questions on Circles asked in CBSE Class X

PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.
In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.
PQ is tangent to a circle with centre O. If \(OQ = a\), \(OP = a + 2\) and \(PQ = 2b\), then relation between \(a\) and \(b\) is
In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
If a regular hexagon ABCDEF circumscribes a circle, then prove that AB + CD + EF = BC + DE + FA.
In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle OAB = 15^\circ \), then \( \angle APB \) equals :
In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle AOB = 130^\circ \), then \( \angle APB \) is equal to :
Prove that the lengths of tangents drawn from an external point to a circle are equal.
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that \( \angle PTQ = 2 \angle OPQ \).
If \(TP\) and \(TQ\) are two tangents to a circle with centre \(O\) from an external point \(T\) so that \(\angle POQ = 120^{\circ}\), then \(\angle PTQ\) is equal to :
In the given figure, \(PA\) is a tangent from an external point \(P\) to a circle with centre \(O\). If \(\angle POB = 125^{\circ}\), then \(\angle APO\) is equal to :
Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.
In the given figure, \(\Delta ABC\) is a right triangle in which \(\angle B = 90^\circ\), \(AB = 4\) cm and \(BC = 3\) cm. Find the radius of the circle inscribed in the triangle \(ABC\).
In the given figure, if a circle touches the side \(QR\) of \(\Delta PQR\) at \(S\) and extended sides \(PQ\) and \(PR\) at \(M\) and \(N\) respectively, then prove that : \(PM = \frac{1}{2}(PQ + QR + PR)\).
PA and PB are tangents drawn to a circle with centre O. If \(\angle AOB = 120^\circ\) and OA = 10 cm, then
PA and PB are tangents drawn to a circle with centre O

(i) Find \(\angle OPA\).
(ii) Find the perimeter of \(\triangle OAP\).
(iii) Find the length of chord AB.
The given figure shows a circle with centre O and radius 4 cm circumscribed by \(\triangle ABC\). BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.
BC touches the circle at D such that BD = 6 cm
If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.
The minute hand of a clock is 21 cm long. The area swept by it in 10 minutes is :
If the area of a sector is one-twelfth that of a complete circle, then the angle of the sector is :
If two tangents inclined at an angle of 60º are drawn to a circle of radius 5 cm, then the length of each tangent is :
A chord of a circle of radius 14 cm subtends an angle of 90° at the centre. Find the area of the corresponding minor and major segments of the circle.
The picture given below shows a circular mirror hanging on the wall with a cord. The diagram represents the mirror as a circle with centre \(O\). \(AP\) and \(AQ\) are tangents to the circle at \(P\) and \(Q\) respectively such that \(AP = 30 \, \text{cm}\) and \(\angle PAQ = 60^\circ\).
Problem Figure
Based on the above information, answer the following questions:
If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.
The minute hand of a clock is 21 cm long. The area swept by it in 10 minutes is :