If the distance of P(x,y) from A(5,1) and B(−1,5) are equal then pove that 3x=2y.
Statement 1 : Let the vertices of a ABC be A(−5,−2),B(7,6), and C(5,−4) . Then the coordinates of the circumcenter are (1,2)˙ Statement 2 : In a right-angled triangle, the midpoint of the hypotenuse is the circumcenter of the triangle.
The vertices of a ΔABC are A(4,6), B(1,5) and C(7,2). A line is drawn to intersect sides AB and AC at D and E respectively, such that ABAD=ACAE=41Calculate the area of the ΔADE and compare it with the area of ΔABC
If a,b,c are the pth,qth,rth terms, respectively, of an HP , show that the points (bc,p),(ca,q), and (ab,r) are collinear.
If a triangle ABC,A≡(1,10), circumcenter ≡(−31,32), and orthocentre ≡(411,34) , then the coordinates of the midpoint of the side opposite to A are (1,−311) (b) (1,5) (1,−3) (d) (1,6)