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Problem of the Week
Problem E
Outside the Path of Totality

Yannick used a camera with a solar filter to capture a solar eclipse. From their location, the Moon blocked some, but not all of the Sun, so they saw a partial solar eclipse. When Yannick enlarged and printed the photo, they noticed that the distance represented by segment \(XY\) in the photo shown was \(70\) cm, and that the diameters of the Sun and the Moon were both \(74\) cm.

A circle with interior coloured grey covers a
large portion of another circle with interior coloured yellow. The two
circles have the same radius and their centres lie along the same
horizontal line. The circles intersect at points X and Y and a dashed
vertical line segment connects X and Y.

Determine the percentage of the Sun that is blocked by the Moon in Yannick’s photo, rounded to \(1\) decimal place.