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

PQ is tangent to a circle with centre O. If \(\angle POR = 65^\circ\), then m\(\angle PTR\) is
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.
Two concentric circles are of radii $5\text{ cm}$ and $4\text{ cm}$. Find the length of the chord of the larger circle which touches the smaller circle.
In two concentric circles with centre O, the radius of outer circle is 25 cm. Chord PQ of the outer circle is tangent to the inner circle at R. If PQ = 14 cm, then the radius of the inner circle is :
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.
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, PA and PB are tangents to a circle centred at O. If \( \angle AOB = 130^\circ \), then \( \angle APB \) is equal to :
In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.
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, 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.
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 :