Suppose `a + b = c + d`, and `a < c`. Use proof by contradiction to show `bged`.

Suppose a,b,c are in AP and a^(2),b^(2),c^(2) are in GP, If agtbgtc and a+b+c=(3)/(2) , than find the values of a and c.

Consider a Delta ABC and let a,b, and c denote the leghts of the sides opposite to vertices A,B and C, respectively. Suppose a=2,b =3, c=4 and H be the orthocentre. Find 15(HA)^(2).

Consider a triangle A B C and let a , b and c denote the lengths of the sides opposite to vertices A , B ,and C , 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

If the integers a,b,c,d are in arithmetic progression and a lt b lt c lt d and d=a^(2)+b^(2)+c^(2) , the value of (a+10b+100c+1000d) is

Suppose a, b and c are distinct and x,y and z are connected by the system of eqations x+ay+a^(2)z=a^(3),x+by+b^(2)z=b^(3) "and" x+cy+c^(2) z=c^(3).

Prove that the points (a, b), (c, d) and (a-c, b-d) are collinear, if ad = bc.

Suppose a, b, c are positive integers with altbltc such that 1//a+1//b+1//c=1 . The value of (a+b+c-5) is …………

If a, b, c and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .