Question

in the figure ABC is a right triangle angled at b , E is the midpoint of AC prove that EA=EB=EC​

Answer 1

Since, E is the mid - point of AC, SO EA = EC. Now, draw a circle circumscribing around the triangle with E as the center and AC as the diameter, you'll notice that wherever on that circle you place B, you _ _ will form a right triangle ABC. So, in other words, you can draw a circle circumscribing the triangle ABC with AC as the diameter. Now, you can observe that EB is also a radius of the circle. Hence, EA = EC = BE.