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.
Question
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.
Solution
Sure, here is the explanation:
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In a right-angled triangle ABC, let's assume that AC is the hypotenuse and B is the right angle.
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The midpoint O of the hypotenuse AC is equidistant from the vertices of the triangle. This is a property of right-angled triangles.
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To prove this, we can draw lines from O to A, B, and C. We'll call these lines OA, OB, and OC.
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Since O is the midpoint of AC, AO = OC. This means that O is equidistant from A and C.
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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.
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Therefore, O is equidistant from A, B, and C.
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