Manhattan GRE prep Geometry Question Help

Graduate School
1

<p>In the MGRE Geometry book I came across the following question:</p>

<p>If angle ACB is 40 degrees and the area of the circle is 81 pi, how long is arc AXB?
The diagram shows an inscibed angle of 40 degrees with points AXC as the arc.</p>

<p>The answer the book gives is 4pi, and it states that Angle ACB an inscribed angle of 40 degrees corresponds to a central angle of 80 degrees, thus arc AXB is equal to 80/360.</p>

<p>My question is wouldn't arc ACB be equal to 80 degrees and arc AXB be equal to a fraction of 80 degrees?</p>

2

<p>HS geometry – Central Angle Theorem. </p>

<p>[Central</a> Angle Theorem - Math Open Reference](<a href=“http://www.mathopenref.com/arccentralangletheorem.html]Central”>Central Angle Theorem - Math Open Reference)</p>