Trigonometry & Inverse Trigonometry
Triangle Properties
Grade 11
Question:
<p>All positions of point <i>P</i> for which triangle <i>DEF</i> is isosceles lie on</p>
<p>(a) the incircle of triangle <i>ABC</i></p>
<p>(b) line of internal angle bisectors from <i>A</i>, <i>B</i> and <i>C</i></p>
<p>(c) arcs of 3 circles</p>
<p>(d) None of the above</p>
Step-by-Step Solution
Key Concept: The locus of points from which perpendiculars to the sides form an isosceles triangle comprises arcs of circles.
<p>For an isosceles triangle <i>DEF</i>, the locus of point <i>P</i> consists of arcs of 3 circles, each centered at a vertex of triangle <i>ABC</i> with appropriate radii determined by the perpendicular distances.</p>
Correct Answer: C