Plane and solid geometry . I h ^D A BJi^ C Ex. 938. Construct a rectangle equivalent to a given rhombus, thedifference of the base and altitude of the rectangle being equal to a givenline Ex. 939. Construct two lines, having given their difference and theirproduct. Ex. 940. Construct a triangle, given its three altitudes. Hint. Con-struct first an auxiliary triangle, with sides x, y^ and 0, such that ha : /?&=y : X and he: ha= x : z. (See Ex. 665.) Ex. 941. Through the vertices of an equilateral triangle draw threelines which shall form an equilateral triangle whose side is eejual to agiven li
Plane and solid geometry . I h ^D A BJi^ C Ex. 938. Construct a rectangle equivalent to a given rhombus, thedifference of the base and altitude of the rectangle being equal to a givenline Ex. 939. Construct two lines, having given their difference and theirproduct. Ex. 940. Construct a triangle, given its three altitudes. Hint. Con-struct first an auxiliary triangle, with sides x, y^ and 0, such that ha : /?&=y : X and he: ha= x : z. (See Ex. 665.) Ex. 941. Through the vertices of an equilateral triangle draw threelines which shall form an equilateral triangle whose side is eejual to agiven line. 242 PLANE GEOMETRY. Ex. 942. The feet of the perpendiculars dropped upon the sides of atriangle from any point in the circumference of the circumscribed circleare collinear. Outline of Proof. The circle havingAP as diameter will pass through iWand Q,•. Z 1 = Z1 and Z 2 = Z 2. Similarly Z3 = Z3, and Z PKM = Z PB3L .-. ZAPB = Z QPK. ,.ZAPQ = ZBPK, .-. ZAMQ = ZBMK, .*. §ikf and iW/i form one str. line. Ex. 943. Given the base, the angle at the vertex, and the sum of the other two sides of a triangle; construct the triangle. Analysis. Imagine the problem solved and drawA ABC. Prolong AB, making BE = BC. since the linec + a is given. Since ZE=IZABC\ A AEC can beconstructed. Ex. 944. The hypotenuse of a right triangle is givenin magnitude and position ; find the locus of the centerof the inscribed circle. Ex. 945. Prove Prop. VIII, Book W^ by using the following figure,in which ADE is placed in the position ADE.
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