3D Geometry
Triangle in 3D Space
Grade 12
Question:
<p>The vertices of △ABC are A(2, 0, 0), B(0, 1, 0), C(0, 0, 2). Its orthocentre is H and circumcentre is S. P is a point equidistant from A, B, C and the origin O. The y-coordinate of S is:</p>
<p>(a) 5/6</p>
<p>(b) 1/3</p>
<p>(c) 1/6</p>
<p>(d) 1/2</p>
Step-by-Step Solution
Key Concept: Circumcentre is equidistant from all vertices of the triangle. Set up equations using distance formula and solve.
The circumcentre S is equidistant from all three vertices A, B, and C. Using the condition SA = SB = SC, the y-coordinate of S is 1/2.
Correct Answer: d