Medians in a circle

Geometry Level 2

In the diagram, let $m=\overline{AF}$ and $n=\overline{FG}$ . Then, choose the answer that represents correctly the arithmetic, geometric and harmonic mean of $m$ and $n$ , respectively.

\overline{BE}

;

\overline{CF}

;

\overline{BC}

\overline{CD}

;

\overline{BE}

;

\overline{DF}

\overline{BE}

;

\overline{DF}

;

\overline{CD}

\overline{BE}

;

\overline{BD}

;

\overline{DF}

1 solution

Anurag Singh
Apr 25, 2014

r=(m+n)/2 AM=(m+n)/2=r=BE GM=(mn)^(1/2). Now, BF=(m-n)/2. Using pythagoras in triangle BDF, we get DF^2=BD^2 - BF^2=m n. Therefore, DF=sq rt of (m n). Hence, the answer is option 2.

Medians in a circle

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