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60 Mins English English25 Questions50 Marks15 Mins English English100 Questions200 Marks60 Mins EnglishThe 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.
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