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The centres of two circles `C_(1) and C_(2)` each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point of the line segment joining the centres of `C_(1) and C_(2)` and C be a circle touching circles `C_(1) and C_(2)` externally. If a common tangent to `C_(1)` and C passing through P is also a common tangent to `C_(2)` and C, then the radius of the circle C, is

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MOTION-CIRCLE-Exercise - 4 | Level - II (Previous Year | JEE Advanced
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  2. Consider, L(1) : 2x + 3y + p – 3 = 0 , L(2) : 2x + 3y + p + 3 = 0, whe...

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  3. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  4. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  5. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  6. Tangents drawn from the point P(1,8) to the circle x^(2) + y^(2) - 6x ...

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  7. The centres of two circles C(1) and C(2) each of unit radius are at a...

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  8. Two parallel chords of a circle of radius 2 are at a distance sqrt3 + ...

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  9. The circle passing through the point (-1,0) and touching the y-axis at...

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  10. The straight line 2x – 3y = 1 divides the circular region x^(2) + y^(2...

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  11. The locus of the mid-point of the chord of contact of tangents drawn f...

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  12. A possible equation of L is (A) x 3y 1 (B) x 3y 1 (C) x 3y 1 (D) x...

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  13. A tangent PT is drawn to the circle x^2+y^2=4 at the point P(sqrt3,1)....

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  14. A possible equation of L is (A) x 3y 1 (B) x 3y 1 (C) x 3y 1 (D) x...

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  15. A circle s passes through the point ( 0,1) and is orthogonal to the ci...

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  16. Let , RS be the diameter of the circle x^(2) + y^(2) = 1 , where S...

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  17. For how many values of p, the circle x^2+y^2+2x+4y-p=0 and the coordin...

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  18. Let T be the line passing the points P(–2, 7) and Q(2,–5). Let F(1) be...

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  19. PARAGRAPH "X" Let S be the circle in the x y -plane defined by the eq...

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  20. Let P be a point on the circle S with both coordinates being positive....

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