Exercises in Geometry

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D.C. Heath, 1909 - Geometry - 81 pages
 

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Page 52 - If two triangles have an angle of one equal to an angle of the other, and...
Page 44 - The square of the bisector of an angle of a triangle is equal to the product of the sides forming the angle diminished by the product of the segments of the third side formed by the bisector.
Page 39 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 40 - In any triangle, the square of the side opposite to an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of these sides and the projection of the other upon that side.
Page 69 - A radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
Page 40 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 48 - The area of a triangle is equal to one half the product of its perimeter by the radius of the inscribed circle.
Page 44 - If two tangents are drawn to a circle at the extremities of a diameter, the portion of any third tangent intercepted between them is divided at its point of contact into segments whose product is equal to the square of the radius.
Page 44 - In any triangle the product of any two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Page 17 - The sum of the perpendiculars dropped from any point in the base of an isosceles triangle to the legs, is equal to the altitude upon one of the arms.

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