Prove That : No tangent can be drawn from the point `(5/2,1)` to the circumcircle of the triangle with vertices `(1,sqrt(3)),(1,-sqrt(3)),(3,-sqrt(3))` .

The incentre of a triangle with vertices (7, 1),(-1, 5) and (3+2sqrt(3),3+4sqrt(3)) is

Find the angles of the triangle whose sides are y+2=0,sqrt(3)x+y=1andy-sqrt(3)x+2+3sqrt(3)=0

Find the angles of the triangle whose sides are (sqrt(3)+1)/(2sqrt(2)), (sqrt(3)-1)/(2sqrt(2)) and sqrt(3)/2 .

The inclination of the line joining the points (3-sqrt(3)) and (sqrt(3),-1) is -

The value of ((1+sqrt3i)/(1-sqrt3i))^64+((1-sqrt3i)/(1+sqrt3i))^64

Simplify : (sqrt(3)+1)^(5)-(sqrt(3)-1)^(5)

In an equilateral triangle, three coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle. The area of the triangle is 2sqrt(3) (b) 6+4sqrt(3) 12+(7sqrt(3))/4 (d) 3+(7sqrt(3))/4

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a) 1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

4 cos^(2)x + sqrt(3) = 2(sqrt(3)+1)

On the line segment joining (1, 0) and (3, 0) , an equilateral triangle is drawn having its vertex in the fourth quadrant. Then the radical center of the circles described on its sides. (a) (3,-1/(sqrt(3))) (b) (3,-sqrt(3)) (c) (2,-1/sqrt(3)) (d) (2,-sqrt(3))