Prove that in an acute triangle ABC, the least values of `Sigma secA` and `Sigma tan^2 A` are 6 and 9 respectively.

ABC is an isosceles triangle right angled at A. forces of magnitude 2sqrt(2),5 and 6 act along BC, CA and AB respectively. The magnitude of their resultant force is

If tan 2A =cot (A-18^(@) ) where 2A is an acute angle , Find the value of A .

In triangle ABC, AD is a median. Prove that AB + AC gt 2AD

In triangle ABC, D is the midpoint of BC. DFZAB and DE bot AC, where points F and E lie on AB and AC respectively. If DF = DE, prove that A ABC is an isosceles triangle.

ABC is a right triangle right angled at B. Let D and E be any points on AB and BC respectively. Prove that AE^(2) + CD^(2) = AC^(2) + DE^(2) .

The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, -5, 7) and (-1, 7, -6), respectively, find the coordinates of the point C.

The vertices of a Delta ABC 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 (AD)/(AB) = (AE)/(AC) = (1)/(4) . Calculate the area of the Delta ADE and compare it with the area of Delta ABC . (Recall Theorem 6 . 2 and Theorem 6 . 6)

In a right trianlge ABC right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that 9(AQ^(2)+BP^(2))= 13AB^(2) .