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7.28 Proving an equal-products problem Prove that if two secants intersect outside a circle, the product of the lengths of one of the secants and its external segment equals the product of the lengths of the other secant and its external segment.

Given: Secants AB and AC. To Prove: AB AD AC AE Plan: Prove nABE , nACD to obtain AB AE . AC AD PROOF:



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If the partners of a rm decide to discontinue the operation of the busi ness, several accounting steps are necessary: 1. The accounts are adjusted and closed. 2. All assets are converted to cash. 3. All creditors are paid in full. 4. Any remaining cash is distributed among the partners according to the balances in their capital accounts (and not according to their prof it and loss ratios).

Reasons A segment may be drawn between any two points. Reflexive property. Angles inscribed in the same arc are congruent. Two triangles are similar if two angles of one triangle are congruent respectively to two angles of the other. 5. Corresponding sides of similar triangles are in proportion. AE 6. In a proportion, the product of the means equals the product of the extremes.





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The only option for HTML authors was the entity  , but this required ve characters to conserve one, not a very economical tradeo In XML, there is now an easy way to maintain this otherwise lost white space This special attribute may be attached to an element to signal the intention that for that element white space should be preserved by applications In valid documents, xml:space, like any other attribute, must be declared if it is used When declared, it must be given as an enumerated type whose only possible values are default and preserve To maintain white space within a document, use the xml:space attribute in conjunction with XSL or CSS and as an attribute declaration: <!ATTLIST element xml:space (default|preserve) choice > This is declared as part of an element declaration in standard fashion.

PRINCIPLE 1:

If two chords intersect within a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other.

Fig. 7-25

If a tangent and a secant intersect outside a circle, the tangent is the mean proportional between the secant and its external segment.

PRINCIPLE 2:

Summary

PRINCIPLE 3:

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If two secants intersect outside a circle, the product of the lengths of one of the secants and its external segment equals the product of the lengths of the other secant and its external segment.

Fig. 7-26

Fig. 7-27

Fig. 7-28

(a) ED (b) AE (c) CE 4. Then 16x EB 4(12), so that 16x 8(2), so x2 x. Then x2 48 or x 16 and x 27(3) or x2 3. 4. 81, and x 9.

Fig. 7-29

1. Partnership and sole proprietorship accounting are alike except in ______. 2. If pro ts and losses are not to be distributed equally, the basis of distribution must be stated in the _______. 3. In order to re ect higher current prices, certain assets of the part nership will be debited, with the corresponding credit to _______. 4. When a partnership decides to go out of business, the process of selling the assets, paying the creditors, and distributing the remaining cash to the partners is known as _______. 5. The nal distribution of cash to the partners is based on their ______. Answers: 1. owner s equity; 2. partnership agreement; 3. asset revalua tion; 4. liquidation; 5. capital

1 72.

Fig. 7-30

The treatment of xml:space depends on the application being used with browsers most likely to preserve the white space desired Ideally, any document that speci es preserve should be presented verbatim, with all white spaces preserved, but this remains to be seen because it is very agent-dependent The default behavior is to ignore white space (tabs, spaces, etc) Therefore, the preserve behavior maintains the intended spacing and formatting that is desired..

PRINCIPLE 1:

The length of the altitude to the hypotenuse of a right triangle is the mean proportional between the lengths of the segments of the hypotenuse.

Thus in right nABC (Fig. 7-31),

Fig. 7-31

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