In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be (a) `5-sqrt(6)` (b) `3sqrt(3)` (c) `5` (d) `5+sqrt(6)`

Two sides of a triangle are of lengths sqrt6 and 4 and the angle opposite to smaller side is 30. How many such triangles are possible? Find the length of their third side and area.

The sides of a triangle are in the ratio 1: sqrt3:2. Then the angles are in the ratio

In a DeltaABC , the median to the side BC is of length 1/sqrt(11-6sqrt3) and it divides the angleA into angles 30^@ and 45@. Find the length of the side BC.

in a triangle with one angle (2 pi )/(3) the lengths of the sides form an A.P if the length of the greater side is 7 cm , then the radius of the circumcircle of the triangle is

Two medians drawn from the acute angles of a right angled triangle intersect at an angle pi/6. If the length of the hypotenuse of the triangle is 3 units, then the area of the triangle (in sq. units) is (a) sqrt3 (b) 3 (c) sqrt2 (d) 9

If the angle A ,Ba n dC of a triangle are in an arithmetic propression and if a , ba n dc denote the lengths of the sides opposite to A ,Ba n dC respectively, then the value of the expression a/csin2C+c/asin2A is 1/2 (b) (sqrt(3))/2 (c) 1 (d) sqrt(3)

The lengths of the tangents from P(1,-1) and Q(3,3) to a circle are sqrt(2) and sqrt(6) , respectively. Then, find the length of the tangent from R(-1,-5) to the same circle.

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 (fig) 4:2sqrt(3) (b) 6+4sqrt(3) 12+(7sqrt(3))/4 (d) 3+(7sqrt(3))/4

Let A B C be a triangle such that /_A C B=pi/6 and let a , ba n dc denote the lengths of the side opposite to A , B ,a n dC respectively. The value(s) of x for which a=x^2+x+1,b=x^2-1,a n dc=2x+1 is(are) -(2+sqrt(3)) (b) 1+sqrt(3) 2+sqrt(3) (d) 4sqrt(3)

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these