Exercises
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1. Given the sum or the difference of any two lines, and the sum of their squares; find the lines.
2. The sum of the squares on two sides AC, CB of a triangle is equal to twice the square on half the base AB, and twice the square on the median which bisects AB.
3. If the base of a triangle be given both in magnitude and position, and the sum of the squares on the sides in magnitude, the locus of the vertex is a circle.
4. If in the △ABC a point D in the base BC be such that
prove that the middle point of AD is equally distant from B and C.
5. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on its diagonals.
PROP. XI.—Problem.