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

' 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 right triangle A B C , right angle at C , M is the mid-point of the hypotenuse A Bdot C is jointed to M and produced to a point D such that D M=C Ddot Point D is joined to point Bdot Show that A M C~= B M D (ii) /_D B C=/_A C B D B C~= A C B (iii) C M=1/2A B

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.

The given figure shows a circle with centre O. P is mid-point of chord AB. Show that OP is perpendicular to AB.

[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).]