Question

If in a $△ABC,AD,BE$ and $CF$ are the altitudes and $R$ is the circumradius, then the radius of the circumcircle of $△DEF$ is

• A. $\frac{R}{2}$
• B. $\frac{2R}{3}$
• C. $\frac{R}{3}$
• D. None of these

Answer 1

The correct option is A $\frac{R}{2}$

The circle that circumcircles $△DEF$ is a Nine-point circle also called Euler's circle.

By property of it, The radius of a triangle's circumcircleis twice the radius of that triangle's nine-point circle.

Hence circumradius of circumcircle of $△DEF=\frac{R}{2}$