Trigonometry & Inverse Trigonometry
Triangle Properties
Grade 11
Question:
<p>In a triangle ABC; AD, BE and CF are the altitudes and R is the circumradius, then the radius of the circle DEF is</p>
<p>(a) 2R</p>
<p>(b) R</p>
<p>(c) \(\frac{R}{2}\)</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: The orthic triangle's circumcircle has radius equal to half the original triangle's circumradius.
<p>The circle DEF is known as the orthic triangle's circumcircle. For any triangle, the circumradius of the orthic triangle (formed by the feet of the altitudes) is \(\frac{R}{2}\), where R is the circumradius of the original triangle ABC.</p>
Correct Answer: C