A direct common tangent is drawn to two circles of radius 25 cm and 20 cm. The centres of the two circles are 35 cm apart. What is the length (in cm) of the tangent?

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.​