In `Delta ABC`,AD is a perpendicular drawn from A to the side BC. If `AD^(2)=BD . CD` , then prove that the triangle is a right-angled triangle.

In any triangle ABC "if" (b+c)/(a)="cot"(A)/(2) , prove that the triangle is right-angled.

In any triangle ABC, if 8R^(2) =a^(2) + b^(2) +c^(2) , prove that, the triangle is right angled.

Answer any One question : In triangleABC , AD is perpendicular on BC and AD^2 = BD . DC, prove that angleBAC is a right angle.

In any triangle ABC, if cosA cos B + sin A sin B sinC =1 then prove that the triangle in an isosceles right angled.

On the outside of the equilateral triangle ABC and in the angular region angleABC , O is a point. OP, OQ and OR are the perpendiculars drawn from O to the sides. AB, BC and CA respectively. Prove that the height of the triangle = OP + OQ - OR.

If in Delta ABC, b = 3 cm, c = 4 cm and the length of the perpendicular from A to the side BC is 2 cm, then how many such triangle are possible ?

If the area of the square drawn on any side of a triangle is equal to the sum of the areas of the squares drawn on the other two sides of the triangle ,then the triangle will be right-angled triangle, the opposite angle of the greatest side of which will be "......................" .

In Delta ABC, /_A is a right angle and AO is perpendicular to BC. Prove that AO^(2) = BO.CO .

In Delta ABC , AD_|_ BC which intersects BC at D. If BD =3 CD , then prove that 2AB^(2) = 2AC^(2)+BC^(2)

I is the incentre of the Delta ABC . The perpendicular drawn from I to BC intersects BC at. P. Prove that AB-AC=BP-CP .