Plane and solid geometry . to it from two fixed points Q and B shall cut off on itequal segments from P. (Hint. See § 24(3.) Ex. 333. Construct the locus of the center of a circle of given radius,which rolls so that it always remains inside of a given triangle and con-stantly touches a side. Do not prove. Ex. 334. Find the locus of a point in one side of a parallelogram andequidistant from two other sides. In what parallelograms is this locus avertex of the parallelogram ? Ex. 335. Find the locus of a point in one side of a parallelogram andequidistant from two of the vertices of the parallelo
Plane and solid geometry . to it from two fixed points Q and B shall cut off on itequal segments from P. (Hint. See § 24(3.) Ex. 333. Construct the locus of the center of a circle of given radius,which rolls so that it always remains inside of a given triangle and con-stantly touches a side. Do not prove. Ex. 334. Find the locus of a point in one side of a parallelogram andequidistant from two other sides. In what parallelograms is this locus avertex of the parallelogram ? Ex. 335. Find the locus of a point in one side of a parallelogram andequidistant from two of the vertices of the parallelogram. In whatclass of parallelograms is this locus a vertex of the parallelogram ? Ex. 336. Construct the locus of the center of a circle of given radiuswhich rolls so that it constantly touches a given circumference. Do notprove. 102 PLANE GEOMETRY Proposition XLIII. Theorem 260. TTie perpendicular bisectors of the sides of a tri^angle are concurrent in a point which is equidistant fromthe three vertices of the Given A ^5(7 with FG, HK, ED, the ± bisectors of AB, BC, prove: (a) FG, HK, ED concurrent in some point as 0;(b) the point 0 equidistant from A, B, and C Argument 1. FG and ED will intersect at some point as 0. 2. Draw OA, OB, and OC. 3o •. O is in FG, the _L bisectorof AB, OB = OA; and•. O is in DE, the X bi-sector of CA, 00 = OA, 4. .-. OB = OC. 5. .*. HK, the _L bisector of BCf passes through 0. 6. •. FG, HK, and ED are con- current in 0. 7. Also 0 is equidistant from A, B, and C. Reasons 1. Two lines J_ respectively to two intersecting linesalso intersect. § 195. 2. Str. line post. I. § 54, 15. 3. Every point in the J« bi- sector of *a line is equi-distant from the ends ofthat line. § 134,4 Ax. 1. § 54, 1. 5. Every point equidistant from the ends of a linelies in the J_ bisector ofthat line. § 139. 6. By def. of concurrent lines § 196. 7. By proof, OA=OB = OC, BOOK I 103 261. Cor. The point of intersection of the perpendic-ular
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