In `triangleABC`, `angleB` is an acute angle and `AD botBC`. Prove that `AC^2= AB^2+BC^2-2BC.BD.`

If triangleABC is an equilateral triangle such that AD bot BC , then AD^2 =

In a isosceles triangle ABC , angleB is right angle. Bisector of angleBAC intersect BC at D. Prove that CD^2= 2BD^2 .

If in triangleABC a=2b and angle A=3 angleB then angleA=

A perpendicular AD is drawn on BC from the vertex A of the acute Delta ABC . Prove that AC^(2) = AB^(2) +BC^(2) -2BC.BD OR Prove that the square drawn on the opposite side of theacute angle of an acute triangle is equal to the areas of the sum of the squares drawn on its other two sides being subtracted by twice the area of the rectangle formed by one of its sides and the projection of the other side to this side.

In triangleABC , anglaBAC = 90^@ , if CD is a median of triangleABC , then prove that BC^2= CD^2+3AD^2 .

In Delta ABC, AD_|_ BC . Prove that AB^(2) - BD^(2) =AC^(2) -CD^(2)

In the isosceles triangle ABC, AB=AC and BE is perpendicular to AC from B. Prove that BC^(2) = 2ACxxCE

In Delta ABC , AD is a median and AM _|_ BC.Prove that (a) AC^(2) = AD^(2) +BC.DM+ ((BC)/(2))^(2) (b) AB^(2) = AD^(2) -BC.DM+ ((BC)/(2))^(2) (c ) AC^(2) + AB^(2) = 2AD^(2) +(1)/(2) BC^(2)

In triangleABC, angleA is right angle and AD bot BC . If AB:AC = 3:4 and AD = 8cm then calculate the length of BD.

In an equilateral triangle ABC, D is a point on side BC such that BD = (1)/(3) BC. Prove that 9 AD^(2) = 7 AB^(2) .