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

The complete question in the attached figure

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

the answer is x=107.96 ft