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It should be noted that in a circle theorem, the angle that's at the center of the circle is twice the angle at the circumference.
<h3>Circle theorem.</h3>An overview of the circle theorem will be given as your information is incomplete. The angle that's in a semicircle is a right angle.
Also, the angles that are in the same segment are equal. Furthermore, the opposite angles that are in a cyclic quadrilateral equal 180°. The angle between the tangent and the radius is also 90°.
Learn more about circles on:
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All the numbers in this range can be written as 
with 
and 
. Construct a table like so (see attached; apparently the environment for constructing tables isn't supported on this site...)
so that each entry in the table corresponds to the sum of the tens digit (row) and the ones digit (column). Now, you want to find the numbers whose digits add to perfect squares, which occurs when the sum of the digits is either of 1, 4, 9, or 16. You'll notice that this happens along some diagonals.
For each number that occupies an entire diagonal in the table, it's easy to see that that number
shows up times in the table, so there is one instance of 1, four of 4, and nine of 9. Meanwhile, 16 shows up only twice due to the constraints of the table.
So there are 16 instances of two digit numbers between 10 and 92 whose digits add to perfect squares.
so that each entry in the table corresponds to the sum of the tens digit (row) and the ones digit (column). Now, you want to find the numbers whose digits add to perfect squares, which occurs when the sum of the digits is either of 1, 4, 9, or 16. You'll notice that this happens along some diagonals.
For each number that occupies an entire diagonal in the table, it's easy to see that that number
So there are 16 instances of two digit numbers between 10 and 92 whose digits add to perfect squares.