[" 5.In the given figure,"AP" bisects "],[qquad [/_CAD" and "/_B=/_C]],[" Prove that "AP|1BC" ."B!=A^(N)>P]

In Figure,AE bisects /_CAD and /_B=/_C . Prove that AE||BC

If a(1/b +1/c) , b(1/c +1/a), c(1/a + 1/b) are in A.P. Prove that a,b,c are in A.P.

a,b and c are in A.P. Prove that b+c , c+a and a+b are in A.P.

If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in A.P., prove that a, b, c, are in A.P.

If a, b, c are in A.P., prove that : b+c,c+a,a+ b are also in A.P.

If a^(2),b^(2) and c^(2) be in A.P. prove that cot A,cot B and cot C are in A.P. also.

If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P, prove that a, b, c are in A.P.

Bisector of /_B and /_C in DeltaABC meet each other at P. Line AP cuts the sides BC at Q. Prove: (AP)/(PQ)=(AB+AC)/(BC) .

If a,b,c are in A.P., prove that a^(2)+c^(2)-2bc=2a(b-c) .

If a (1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P. Prove that a, b, c are in A.P.