If the vertices of a triangles are O(0, 0), A (a, 0) and B(0, a). Then, the distance between its circumcenter and orthocenter is:

Explanation: Step 1: Identify the Triangle The vertices are: — lies on the x-axis. — lies on the y-axis. Since the sides and lie along the coordinate axes, the angle at the origin is . This means is a right-angled triangle at . Step 2: Locate the Orthocenter In a right-angled triangle, the orthocenter is the vertex where the right angle is formed. Since the right angle is at , the orthocenter is: Step 3: Locate the Circumcenter In a right-angled triangle, the circumcenter is the midpoint of the hypotenuse ( ). Using the midpoint formula for and : Step 4: Calculate the Distance between and Using the distance formula between and :

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