A circle centered at P with radius 4 cm and another centered at Q with radius 16 cm touch each other externally. A third circle with centre R is drawn to touch the first two circles. they all have a common tangent. Then the radius of the circle with centre R is
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Given two circles are 5 and 6.
The blue circles numbered 1 to 4 are all possible solutions. These are infinite in number. They are within circle 5 or circle 6. Also they are outside circle 5 and outside circle 6.
The centers of all circles ie., P, Q and R are collinear.
obviously the common tangent is perpendicular to the line joining all centers of all circles. Also you find two more circles numbered 7 and 8., These are tangentially touching circles 5 and 6, as well as the common tangent of circles 5 and 6.
The blue circles numbered 1 to 4 are all possible solutions. These are infinite in number. They are within circle 5 or circle 6. Also they are outside circle 5 and outside circle 6.
The centers of all circles ie., P, Q and R are collinear.
obviously the common tangent is perpendicular to the line joining all centers of all circles. Also you find two more circles numbered 7 and 8., These are tangentially touching circles 5 and 6, as well as the common tangent of circles 5 and 6.
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