WBJEE · Maths · Properties of Triangles
If in a \(\triangle A B C, A D, B E\) and \(C F\) are the altitudes and \(R\) is the circumradius, then the radius of the circumcircle of \(\Delta D E F\) is
- A \(\frac{R}{2}\)
- B \(\frac{2 R}{3}\)
- C \(\frac{R}{3}\)
- D None of these
Answer & Solution
Correct Answer
(A) \(\frac{R}{2}\)
Step-by-step Solution
Detailed explanation
Let circumradius of \(\Delta\) DEF be \(R'\) We know. \(\angle F D E=180^{\circ}-2 A\) and \(F E=R \sin 2 A\) Now, by sine rule in \(\triangle D E F\) \(2 R^{\prime}=\frac{E F}{\sin \angle F D E}=\frac{A \sin 2 A}{\sin \left(180^{\circ}-2 A\right)}\) \(\therefore\)…
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