Find the distance (in cm) between the centres of two circles having radii of 40 cm and 30 cm, respectively, if the length of a/an transverse/indirect common tangent to the two circles is given as 10√15 cm.

The length of each of two tangents drawn from an external point to a circle is 10 cm. What is the approximate distance from the external point to the center of the circle, if the radius is 6 cm?

Two circles with radii 6 cm and 2 cm have their centers 10 cm apart. How many common tangents can be drawn between them, and what type(s) of tangents are they?

A circle with radius x touches another circle with radius 2x externally. What is the length of a direct common tangent?

Two circles have radii of 12 cm and 4 cm. If the length of a direct common tangent is 15 cm, what is the distance between their centers?

The distance between the centers of two circles is d. The lengths of their direct and transverse common tangents are L and M, respectively. If L² + M² = 200 and the sum of the squares of their radii is 100, what is the value of d?

AP and AQ are two tangents drawn to a circle with center O from an external point A. If ∠PAQ = 40°, then ∠POQ is:

​In the given figure, if PB = 20 cm and OA= 15 cm, then find the shortest distance between the circle and P.​