Question 172885
Find the radius of a circle if a 48-meter chord is 7 meters from the center


Draw a circle and draw the chord horizontally across the bottom of the circle. Draw the segment from the center of the circle to the midpoint of the chord. It is 7 m long by the problem's definition and forms a right triangle with the chord. You now have a right triangle and know the lengths of the two legs. The radius of the circle is the hypotenuse of the triangle. Its length can be calculated from the Pythagorean theorem.

{{{a^2 + b^2 = c^2}}}
{{{7^2 + 24^2 = c^2}}}
{{{49+576=c^2}}}
{{{625=c^2}}}
c=25

The radius is 25 m.