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

The sides AB and BC and the median AD of triangle ABC are equal to the sides PQ and QR and the median PM of triangle PQR respectively. Prove that the triangles ABC and PQR are congruent.

If the lengths of the sides of a triangle are 3, 5, 7 , then its largest angle of the triangle is

In a triangle the length of the two larger sides are 24 and 22, respectively.If the angles are in A.P.,then the third side ,is

A right triangle has hypotenuse of length p\ c m and one side of length q\ c m . If p-q=1 , find the length of the third side of the triangle.

In triangle PQR. angleQ is a right angle, QR=24, and PR=26. Triangle YXZ is similar to triangle PQR, where vertices X, Y, and Z correspond to vertices P, Q, and R, respectively, and each side of triangle XYZ is (1)/(2) the length of the corresponding side of triangle PQR. What is the value of sin Z?

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 ?

In a triangle PQR, the side QR is extended to S to form the exteiror angle PRS of measure 120^(@) . If the sides PQ and PR are equal, then prove that the triangle PQR is an equilateral triangle.

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 Detla ABC , then the value of abc(a+b+c)(Delta')/(Delta^(3)) is (a) 1 (b) 2 (c) 3 (d) 4