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

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 ?

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)

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))

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

[ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle.Explain why O is equidistant from A ,B and C .(The dotted lines are drawn additionally to help you).]