The Elements of Geometry

Cover The Elements of Geometry
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If one leg of a right triangle is double the other, the perpen- dicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4.
23. If two parallels to the side BC of a triangle ABC meet the sides AB and AC in D and F, and E and , respectively, prove BD ^_ BF = DF CE CG EG' 24. C and D are the middle points of a chord AB and its sub- tended arc. If AD = 12 and CD = 8, what is the diameter of the circle ?
25. If AD and BE are the perpendic
...ulars from the vertices A and B of the triangle ABC to the opposite sides, prove that AC:DC= BC'. EC: 26. If D is the middle point of the side BC of the triangle AB C, right-angled at C, prove that AB 2 AD 2 = 3 ~CD*.
27. The diameters of two concentric circles are 14 arid 50 units, respectively. Find the length of a chord of the greater circle which is tangent to the smaller.
28. The length of a tangent to a circle from a point 8 units dis- tant from the nearest point of the circumference, is 12 units.


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