Plane and solid geometry . A b Given A ABC, with area T, sides a, by and c, and radius ofinscribed circle r. To prove r= ^ {a + b + c)T, Outline of Proop 1. Area of A OBC=:\ a • r; area of A OCA = i- 6 . r; areaoi AOAB = \ c-r. 2. ., T^^{a + h + c)r. 492. Cor. The area of any polygon circumscribedabout a circle is equal to one half its perimeter multi-plied by the radius of the inscribed circle. 224 PLANE GEOMETFwY. (6) In like manner, reduce the number of sides of the new-polygon GCDEF until A DHK is obtained. The construction, proof, and discussion are left as an exercisefor the stude
Plane and solid geometry . A b Given A ABC, with area T, sides a, by and c, and radius ofinscribed circle r. To prove r= ^ {a + b + c)T, Outline of Proop 1. Area of A OBC=:\ a • r; area of A OCA = i- 6 . r; areaoi AOAB = \ c-r. 2. ., T^^{a + h + c)r. 492. Cor. The area of any polygon circumscribedabout a circle is equal to one half its perimeter multi-plied by the radius of the inscribed circle. 224 PLANE GEOMETFwY. (6) In like manner, reduce the number of sides of the new-polygon GCDEF until A DHK is obtained. The construction, proof, and discussion are left as an exercisefor the student. Ex. 845. Transform a scalene triangle into an isosceles triangle. Ex. 846. Transform a trapezoid into a right triangle. Ex. 847. Transform a parallelogram into a trapezoid. Ex. 848. Transform a pentagon into an isosceles triangle. Ex. 849. Construct a triangle equivalent to f of a given trapezium. Ex. 850. Transform 4 of a given pentagon into a triangle. Ex. 851. Construct a rhomboid and a rhombus which are equivalent,and which have a common diagonal. Proposition VII. Theorem 495. Tlve area of a trapezoid equals the product of itsaltitude and one half the sum of its bases. b
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
