1
IIT-JEE 1987
Subjective
+4
-0
The circle $${x^2}\, + \,{y^2} - \,4x\, - 4y + \,4 = 0$$ is inscribed in a triangle which has two of its sides along the co-ordinate axes. The locus of the circumcentre of the triangle is $$x\, + \,y\, - xy\, + k\,{\left( {{x^2}\, + \,{y^2}} \right)^{1/2}} = 0$$. Find k.
2
IIT-JEE 1987
Subjective
+3
-0
Let a given line $$L_1$$ intersects the x and y axes at P and Q, respectively. Let another line $$L_2$$, perpendicular to $$L_1$$, cut the x and y axes at R and S, respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin.
3
IIT-JEE 1987
Fill in the Blanks
+2
-0
A polygon of nine sides, each of length $$2$$, is inscribed in a circle. The radius of the circle is .................
4
IIT-JEE 1987
MCQ (More than One Correct Answer)
+2
-0.5
In a triangle, the lengths of the two larger sides are $$10$$ and $$9$$, respectively. If the angles are in $$AP$$. Then the length of the third side can be
A
$$5 - \sqrt 6 $$
B
$$3\sqrt 3 $$
C
$$5$$
D
$$5 + \sqrt 6 $$
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