In a triangle PQR, P is the largest angle and `cosP=1/3`. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

In DeltaABC , the incircle touches the sides BC, CA and AB, respectively, at D, E,and F. If the radius of the incircle is 4 units and BD, CE, and AF are consecutive integers, then the value of s, where s is a semi-perimeter of triangle, is ______

P(3,4), Q(7,2) and R(-2, -1) are the vertices of PQR. Write down the slope of each side of the triangle.

In right angle triangle Delta PQR ,right angle at Q,PQ = 6cm and angle RPQ =60^(@) Determine the lengths of QR and PR.

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If AC = 1, then the length of the median of triangle ABC through the vertex A is equal to

In a triangle PQR, let anglePQR = 30^(@) and the sides PQ and QR have lengths 10 sqrt3 and 10, respectively. Then, which of the following statement(s) is (are) TRUE ?

Let the incircle of a Delta ABC touches sides BC, CA and AB at D,E and F, respectively. Let area of Delta ABC be Delta and thatof DEF be Delta' . If a, b and c are side of Dela ABC , then the value of abc(a+b+c)(Delta')/(Delta^(3)) is

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

The lengths of the tangents drawn from the vertices A, B and C to the incicle of DeltaABC are 5, 3 and 2, respectively. If the lengths of the parts of tangents within the triangle which are drawn parallel to the sides BC, CA and AB of the triangle to the incircle are alpha, beta and gamm , respectively, then the value of [alpha + beta + gamma] (where [.] respresents the greatest integer functin) is _____

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is