## Realated Questions

Three horses are grazing within a semi-circular field. In the diagram given below, AB is thediameter of the semi -circular field with centre at O. Horses are tied up at P, R and S such that PO and RO are the radii of semi -circles with centers at P and R respectively, and S is the centre of the circle touching the two semi -circles with diameters AO and OB. The horses tied at P and R can graze within the respective semi -circles and the horse tied at S can graze within the circle centred at S. The percentage of the area of the semi-circle with diameter AB that cannot be grazed by the horses is nearest to

Three circles of equal radii have been drawn inside an equilateral triangle, of side a, such that each circle touches the other two circles as well as two sides of the triangle. Then, the radius of each circle is

If l+m+n=0, which of the following conditions must l, m and n satisfy so that the system of simultaneous linear equations x+3y-4z=l, 2x-y-z=m, x+y-2z=n has at least one ?