Trigonometry & Inverse Trigonometry
Triangle Centers
Grade 11
Question:
<p>If triangle <i>DEF</i> is equilateral, then <i>P</i></p>
<p>(a) coincides with incentre of triangle <i>ABC</i></p>
<p>(b) coincides with orthocentre of triangle <i>ABC</i></p>
<p>(c) lies on pedal triangle of <i>ABC</i></p>
<p>(d) None of the above</p>
Step-by-Step Solution
Key Concept: The equilateral pedal triangle is obtained only when the point is at the incentre, which maintains equal perpendicular relationships.
<p>When the triangle formed by the feet of perpendiculars is equilateral, the point <i>P</i> must be positioned such that it has equal angular distances to all three sides. This occurs uniquely at the incentre of triangle <i>ABC</i>, where all angle bisectors meet.</p>
Correct Answer: A