p^(2)x^(2)+c^(2)x^(2)-ac^(2)-ap^(2)

if the square of the length of the tangents from point P to the circleS x^(2)+y^(2)=a^(2), x^(2)+y^(2)=b^(2), x^(2)+y^(2)=c^(2) are in A.P. Then a^(2), b^(2), c^(2) are is

If the square of the length of the tangents from a point P to the circles x^(2)+y^(2)=a^(2), x^(2)+y^(2)=b^(2), x^(2)+y^(2)=c^(2) are in A.P. then a^(2),b^(2),c^(2) are in

If the square of the length of the tangents from a point P to the circles x^(2)+y^(2)=a^(2), x^(2)+y^(2)=b^(2), x^(2)+y^(2)=c^(2) are in A.P. then a^(2),b^(2),c^(2) are in

If the squares of the lengths of the tangents from a point P to the circles x^(2)+y^(2)=a^(2) , x^(2)+y^(2)=b^(2) , x^(2)+y^(2)=c^(2) are in A.P then a^(2),b^(2),c^(2) are in

The determinant Delta=|{:(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2)):}| is divisible by

The determinant Delta=|{:(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2)):}| is divisible by

Show that |(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2))| is divisible by x^(2) .

Show that (a^(2) +ab+b^(2)) ,(c^(2) +ac +a^(2)) and ( b^(2) +bc+ c^(2)) are in AP, if a,b,c are in AP.

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).