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?

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?

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?

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.​