Circumcentre of triangle `A B C`, where A(rsinx,rcosx), B (rainy, rcosy), C(rsinz,rcosz)

Find the circumcentre of triangle ABC if A (7, 4), B (3, -2) and angle C = (pi)/(3) .

The circumcentre of a triangle having vertices A(a,atan alpha),B(b,btan beta),C(c,ctan gamma) is at origin, where alpha+beta+gamma =pi . Then the orthocentre lies on

The area of a triangle with vertices (a,b+c), (b,c+a) and (c,a+b) is

The coordinates of the circumcentre of the triangle formed by the points O\ (0,\ 0) , A(a ,\ 0) and B(0,\ b) are (a ,\ b) (b) (a/2, b/2) (c) (b/2, a/2) (d) (b ,\ a)

D , E , F are the foot of the perpendicular from vertices A , B , C to sides B C ,\ C A ,\ A B respectively, and H is the orthocentre of acute angled triangle A B C ; where a , b , c are the sides of triangle A B C , then H is the incentre of triangle D E F A , B ,\ C are excentres of triangle D E F Perimeter of D E F is a cos A+b cos B+c\ cos C Circumradius of triangle D E F is R/2, where R is circumradius of A B C

If the incircel of the triangle ABC, through it's circumcentre, then the cos A + cos B + cos C is

Find the length of altitude through A of the triangle A B C , where A-=(-3,0)B-=(4,-1),C-=(5,2)

Find the length of altitude through A of the triangle A B C , where A-=(-3,0)B-=(4,-1),C-=(5,2)

Let the orthocentre and centroid of a triangle be A(-3,5) and B(3,3) respectively. If C is the circumcentre of the triangle then the radius of the circle having line segment AC as diameter, is

In triangle ABC, prove that (b/c+c/b) cosA +(a/b+b/a) cos C+(a/c+c/a)cosB=3