The length of a tangent from a point d cm away from the centre of a circle of radius ‘r’ is

Two concentric circles are of radii a and b (a>b). Length of the chord of the larger circle which touches the small circle is

If AP and AQ are two tangents to a circle with centre O so that $\mathrm{\angle }POQ\backslash angle\; POQ$= 110°, then $\mathrm{\angle }PAQ\backslash angle\; PAQ$ =

The shaded portion represents

Number of chords of a circle is

In the adjacent figure if PA = 4 cm, BP = 3 cm and AC = 11 cm then BC =

The distance between two parallel tangents to a circle of diameter 8 cm is

The length of the tangent from an external point A on a circle with centre O is

A tangent PA touches a circle with centre ‘O’ at A, then

In the figure XY and $X{Y}^{1}XY^1$ are two parallel tangents to a circle with centre ‘O’ and other tangent AB with point of contact ‘C’ intersecting XY at A and XY' at B, then ∠AOB =