Question

Circle O has diameter FG and chord FH. Calculate the measure of < HFG if GH = 72°

Answer 1

Given the figure in the attached image.

Circle O has diameter FG and chord FH.

If arc GH is;

$GH=72^{\circ}$

we want to find the measure of angle HFG.

Recall that from circle geometry theorems;

"The angle at the center of a circle is twice the angle at the circumference of the circle."

So;

$\begin{gathered} 2\times m\measuredangle HFG=m\measuredangle GOH \\ m\measuredangle HFG=\frac{1}{2}m\measuredangle GOH \\ m\measuredangle HFG=\frac{1}{2}GH \end{gathered}$

substituting the value of GH;

$undefined$