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class Point ( public: Point(float x=0, float y=O, float z=O) : x (x), y-(y), z-(z) ( } Point(const Point& p) : x-(p.x->, y-(p.y-), z-(p.z-) { } void negate0 { x- *= -1; y- *= -1; z- *= -1; } double norm0 { return sqrt(x - *x- + y -*y - + z-*z -); } void print0 / { tout << ' ( ' << x- << I', " << y- << I', " << z- << I') I'; } private: L float x-, Y-, z-; 1 ; In this implementation, we have used the common device of ending the name of each data member with an underscore (-). This has the advantage of making it easy to match up the names of constructor parameters (x, y, and z) with their corresponding data members (x-, y-, and z -) without conflict. 8.18 Implement a Stack class for stacks of ints. Include a default constructor, a destructor, and the usual stack operations: push ( ) , pop ( ) , isEmpty( >, and isFull(). use an array

Fig. 15-39

class Stack { public: Stack(int s=lO) : size(s), top(-1) { a = new int[size]; } -Stack0 ( delete [] a; } void push(const int& item) { a[++top] = item; } int pop0 { return a[top--I; } int isEmpty const ( return top == -1; } int isFull() const { return top == (size-l); } private: int size; // size of array int top; // top of stack int* a; // array to hold stack items

15.20. Circumscribe and inscribe circles about (a) an acute triangle; (b) an obtuse triangle. 15.21. Circumscribe a circle about (a) a right triangle; (b) a rectangle; (c) a square. 15.22. Construct the inscribed and circumscribed circles of an equilateral triangle. 15.23. Locate the center of a circle drawn around the outside of a half-dollar piece.

In this implementation, top is always the index of the top element on the stack. The data member s i z e is the size of the array that holds the stack items. So the stack is full when it contains that number of items. The constructor sets s i z e to 10 as the default.

IZ = Int(X ^ 2 Y ^ 2)

(15.9) (15.9) (15.9) (15.9)

8.19 Implement a Time class. Each object of this class will represent a specific time of day, storing

the hours, minutes, and seconds as integers. Include a constructor, access functions, a function advance(int h, int m, int s ) to advance the current time of an existing object, a function reset(int h, int m, int s ) to reset the current time of an existing object, and a print ( ) function

15.24. In a given circle, inscribe (a) a square; (b) a regular octagon; (c) a regular 16-gon; (d) a regular hexagon; (e) an equilateral triangle; (f) a regular dodecagon. 15.25. Construct a triangle similar to a given triangle with a base (a) three times as long; (b) half as long; (c) one and one-half times as long. (15.10)

class Time { public: Time(int h=O, int m=O, int s=O) : hr(h), min(m), set(s) { normalize(); } int hours0 { return hr; } int minutes0 { return min; > int seconds0 { return set; > void advance(int, int, int); void reset(int, int, int); void print0 { tout -CC hr CC II:" CC min CC '7' CC set; private: int hr, min, set; void normalize(); 1 ; void Time: :normalize() min += set/60; hr += min/60; hr = hr % 24; min = min % 60; set = set % 60;

The theorems proved in this chapter are considered the most important in the logical sequence of geometry They are as follows: 1 If two sides of a triangle are congruent, the angles opposite these sides are congruent (Base angles of an isosceles triangle are congruent) 2 The sum of the measures of the angles in a triangle equals 180 3 If two angles of a triangle are congruent, the sides opposite these angles are congruent 4 Two right triangles are congruent if the hypotenuse and a leg of one are congruent to the corresponding parts of the other 5 A diameter perpendicular to a chord bisects the chord and its arcs 6 An angle inscribed in a circle is measured by one-half its intercepted arc 7 An angle formed by two chords intersecting inside a circle is measured by one-half the sum of the intercepted arcs 8a.

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