In the adjacent figure, `Delta ABC` is right angled at C and `DE bot AB`. Prove that `Delta ABC ~ Delta ADE` and hence find the lengths of AE and DE ?

In the figure, if BD bot AC and CE bot AB , prove that (i) Delta AEC~ Delta ADB " " (ii) (CA)/(AB)=(CE)/(DB)

Delta ABC is circumscribing a circle. Find the length of BC.

In Delta ABC , if DE|| BC, AD=x DB=x-2, AE= x+2 and EC=x-1 then find the length of the sides AB and AC.

In the adjacent figure, ABC is a right angled triangle with right angle at B and points D, E trisect BC. Prove that 8AE^(2)=3AC^(2)+5AD^(2).

ABC is a right triangle , right angled at A and D is the mid point of AB . Prove that BC^(2) =CD^2 +3BD^(2) .

Let the lengths of the altitudes drawn from the vertices of Delta ABC to the opposite sides are 2, 2 and 3. If the area of Delta ABC " is " Delta , then find the area of triangle

In the adjacent figure, ABC is a triangle in which angleB = 50^(@) and angleC = 70^(@) . Sides AB and AC are produced. If ‘z’ is the measure of the angle between the bisectors of the exterior angles so formed, then find 'z'.

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(2) .