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

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

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)

Find a point on the base of a scalene triangle equidistant from its sides.

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.

If D is the mid-point of the hypotenuse A C of a right triangle A B C , prove that B D=1/2A C

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.

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 that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle