ABC is a right-angled triangle and O is the midpoint of the side opposite to the right angle.Explain why O is equidistant from A, B, and C.

Sure, here is the explanation:

1. In a right-angled triangle ABC, let's assume that AC is the hypotenuse and B is the right angle.

2. The midpoint O of the hypotenuse AC is equidistant from the vertices of the triangle. This is a property of right-angled triangles.

3. To prove this, we can draw lines from O to A, B, and C. We'll call these lines OA, OB, and OC.

4. Since O is the midpoint of AC, AO = OC. This means that O is equidistant from A and C.

5. Now, let's consider OB. Since ABC is a right-angled triangle and O is the midpoint of the hypotenuse, OB is a line of symmetry. This means that OB is equal to OA and OC.

6. Therefore, O is equidistant from A, B, and C.