List of top Mathematics Questions on Number of Tangents from a Point on a Circle

Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that \(\angle\) APB = 2 \(\angle\) OAB.
In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If \(\angle QPR = 60^{\circ}\), then the length of each tangent is :
Solve any one of the following internal choices (a) or (b):
31(a) Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that $\angle APB = 2 \angle OAB$.
In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If $\angle QPR = 60^\circ$, then the length of each tangent is :
If two tangents inclined at an angle of \(60^\circ\) are drawn from an external point to a circle of radius 6 cm, then the length of each tangent is :
PQ is tangent to a circle at a point P on the circle. The number of tangents which can be drawn to the circle parallel to PQ, is
In Fig. 10.13, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ∠AOB = 90°.
XY and X'Y' are two parallel tangents to a circle with centre O
Fig. 10.13
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Prove that the parallelogram circumscribing a circle is a rhombus.
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC
A quadrilateral ABCD circumscribe a circle
Fig. 10.12
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to
In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to
a circle with the two tangents TP and TQ
Fig. 10.11
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is