the circular stone mound in Ireland called Newgrange has a diameter of 250 feet. A passage 62 feet long leads toward the center of the mound. Find the perpendicular distance x from the end of the passage to either side of the mound
we know that If two chords intersect in the interior of a circle, then
the product of the lengths of the segments of one chord
is equal to the product of the lengths of the segments of
the other chord (Segments of Chords Theorem)
therefore
AB*BC=DB*BE AB=x BC=x DB=62 BE=250-62---------> BE=188 ft
so x*x=62*188----------> x²=11656--------> x=√11656--------> x=107.96 ft
