JEE Advanced 2023 Mathematics question
Let be the circle of radius 1 with center at the origin. Let be the circle of radius with center at the point , where . Two distinct common tangents and of and are drawn. The tangent touches at and at . The tangent touches at and at . Mid points of the line segments and are joined to form a line which meets the -axis at a point . If , then the value of is .
Answer: 2
Solution
The midpoint of a common tangent segment has equal tangent lengths to both circles, so both midpoints lie on the radical axis: . It
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