`Prove that the mid-point of the hypotenuse of a right triangle is equidistant from its vertices.

Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices.

Prove by the vector method that the mid-point of the hyptenuse of a right angled triangleis equidistant from the vertices of the triangle.OR

In Fig.14.40, a right triangle BOA is given.C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O,A and B.( FIGURE)

What is the measure of the hypotenuse of a right triangle, when its medians, drawn from the vertices of the acute angles, are 5 cm and 2 sqrt(10) cm

What is the measure of the hypotenuse of a right triangle, when its medians, drawn from the vertices of the acute angles, are 5 cm and 2sqrt(10) cm long ?

Prove that the line segment joining the mid- point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.

A point on the hypotenuse of a right triangle is at distances a and b from the sides of the triangle.Show that the minimum length of the hypotenuse is (a^((2)/(3))+b^((2)/(3)))^((3)/(2))

Prove by vector method, that in a right-angled triangle ABC, AB^(2) + AC^(2) = BC^(2) , the angle A being right angled. Also prove that mid-point of the hypotenuse is equidistant from vertex.

If D is the mid-point of the hypotenuse AC of a right triangle ABC, prove that BD=(1)/(2)AC