Let $$\mathrm{ABCD}$$ be a quadrilateral with area 18 , with side $$\mathrm{A B}$$ parallel to the side $$\mathrm{C D}$$ and $$\mathrm{A B}=2 \mathrm{CD}$$. Let $$\mathrm{AD}$$ be perpendicular to $$\mathrm{AB}$$ and $$\mathrm{CD}$$. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is :
Match the statements in Column I with the properties Column II.
| Column I | Column II | ||
|---|---|---|---|
| (A) | Two intersecting circles | (P) | have a common tangent |
| (B) | Two mutually external circles | (Q) | have a common normal |
| (C) | Two circles, one strictly inside the other | (R) | do not have a common tangent |
| (D) | Two branches of a hyperbola | (S) | do not have a common normal |
Tangents are drawn from the point (17, 7) to the circle $$x^2+y^2=169$$.
Statement 1 : The tangents are mutually perpendicular.
Statement 2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is $$x^2+y^2=338$$
A circle touches the line $L$ and the circle $C_1$ externally such that both the circles are on the same side of the line, then the locus of center of the circle is:
JEE Advanced Subjects
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