Properties of Triangle Questions

Let PS be the median of the triangle with vertices P(2, 2), Q(6, - 1) and R (7, 3). The equation of the line passing through (1, - 1) and parallel to PS is

In a triangle the sum of two sides is x and the product of the same two sides is y. If x2 - c2 = y, where c is the third side of the triangle, then the ratio of the in radius to the circum-radius of t...

Let ᐃPQR be a triangle. Let and . If || = 12, ||= 4√3 and . = 24 then which of the following is (are) true ?...

Let PQR be a triangle of area ᐃ with a = 2, b = and c = , where a, b, and c are the lengths of the sidesof the triangle opposite to the angles at P, Q and R respectively. Then equals...

Three distinct points A, B and C are given in the 2 - dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (-1, 0) i...

ABC is a triangle, right angled at A. The resultant of the forces acting along with magnitudes and respectively is the force along , where D is the foot of the perpendicular from A onto BC. The magnit...

The values of a, for which the points A, B, C with position vectors and respectively are the vertices of a right-angled triangle with C = are...

In a triangle PQR, ∠R = . If tan and tan are the roots of ax2 + bx + c = 0, a ≠ 0 then...

In a triangle ABC, let ∠C = If r is the inradius and R is the circumradius of the the triangle ABC, then 2 (r + R) equals...

Let A (2, -3) and B(-2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

Let z1 and z2 be two roots of the equation z2 + az + b = 0, z being complex. Further, assume that the origin, z1 and z2 form an equilateral triangle, then...

If in a triangle ABC a cos + c cos2 = , then the sides a, b and c...

In a triangle ABC, medians AD and BE are drawn. If AD = 4, ∠DAB = and ∠ABE = , then the area of the ᐃ ABC is...

The vectors , and are the sides of a triangle ABC. The length of the median through A is...

A triangle with vertices (4, 0), (-1, -1), (3, 5) is

In a triangle with sides a, b, c, r1 > r2 > r3 (which are the ex - radii) then

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are...

If the points A(z), B(-z) and c(1 - z) are the vertices of an equilateral triangle ABC then Re(z) is equal to :-

If P is a moving point in the xy-plane in such a way that perimeter of triangle PQR is 16 {where Q ≡ (3, √5), R ≡ (7, 3 √2)} then maximum area of triangle PQR is :-...

Let be a unit vector and is a nonzero vector not parallel to . The angles of the triangle, two of whose sides are represented by and are...