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Plan: Circumscribe a circle and show that angles BAC, CAD, and DAE are congruent. PROOF:

ios: :skipws ios: :left ios: :right ios: :internal ios: :dec ios: : act ios: :hex ios: :showbase ios: :showpoint ios:: uppercase ios: :showpos ios: :scientific ios: :fixed ios: :unitbuf ios: :stdio

Skip leading white space during formatted input. (default) Left-justify output, padding on right to make required width. Right-justify output, padding on left to make required width. (default) Right-justify numeric output, left-justify any sign or radix, and pad the middle to make required width. Input and output integers base 10. (default for output) Input and output integers base 8. Input and output integers base 16. Output integers with radix prefix; e.g., 027 for (act), 0x2~1 for (hex). (default) butput real numbers with decimal point and trailing zeros. Use uppercase letters to output hex integers and reals in scientific. Prefix positive integers with 1 1 + . Output real numbers in scientific notation; e.g., 1.2 3 45 6e- 0 9 Output real numbers with n digits to right of decimal point, where rz is the precision (Jrec) Flush the output stream after each insertion. Flush stdio and stderr after each insertion.

Statements 1. ABCDE is a regular pentagon. 2. Circumscribe a circle about ABCDE. 3. BC CD DE 4. BC > CD >DE 5. /BAC /CAD /DAE

The flags ( > function sets the stream s flags to the new setting without retaining any of the previous settings. So it has the effect of clearing all the flags that are not named in the function s argument. In Example 12.4, the second call to tout . flags ( > cleared the three settings made by the first call. To set one or more flags without clearing any others, use the set f ( ) function, which is one of the three other member functions defined in ios for accessing the format flags:

lblHello(4).Caption = "Buon Giorno" lblHello(5).Caption = "Konichihua" lblHello(6).Caption = "Buenos Dias" Command1(0).Caption Command1(1).Caption Command1(2).Caption Command1(3).Caption Command1(4).Caption = = = = = "Go" "Clear" "Add" "Delete" "Quit"

Reasons 1. Given 2. A circle may be circumscribed about any regular polygon 3. A regular polygon is equilateral. 4. In a circle, equal chords have equal arcs. 5. In a circle, inscribed angles having congruent arcs are congruent. 6. To divide into three congruent parts is to trisect.

class ios { public: // previous members included here long setf(long f) { long t = -flags; -flags I= f; return,t; > long setf(long f, long mask) { long t = -flags; - flags = ( - flags & -mask) 1 (f & mask); return t; > long unsetf(long mask) { long t = _ flags & mask; - flags SC= -mask; return t;. } // more members included here

In the regular hexagon, square, and equilateral triangle, special right triangles are formed when the apothem r and a radius R terminating in the same side are drawn. In the case of the square we obtain a 45 -45 -90 triangle, while in the other two cases we obtain a 30 -60 -90 triangle. The formulas in Fig. 10-4 relate the lengths of the sides and radii of these regular polygons.

The next example shows how to use the one-argument set f ( > function to set flags without clearing others.

Fig. 10-4

EXAMPLE 12.5 Using cou t . set f ( ) to Set a Stream s Format Flags This example is the same as Example 12.4 except that set f ( ) is called instead of f lags ( ) . main0 1 int n = 234; long oldf = cout.setf( ios::hex I ios::uppercase ); tout cc n CC endl; cout.setf( ios::hex I ios:: showbase ); tout CC n cc endl; cout.flags(oldf); tout CC n CC endl;

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