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Provide the proofs requested in Fig. 6-45. Please refer to figure 6-45(a) for problems 6.2(a) and (b); to figure 6-45(b) for problems 6.2(c) and (d); and figure 6-45(c) for problems 6.2(e) and (f). (6.3) (a) Given: AB AC To Prove: ABC > ACB (b) Given: ABC > ACB To Prove: AB AC (c) Given: Circle O, AB AD Diameter AC To Prove: BC CD (d) Given: Circle O AB AD, BC CD To Prove: AC is a diameter. (e) Given: AD BC To Prove: AC BD (f) Given: AC BD To Prove: AD BC

Fig. 6-45



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Prove each of the following: (a) If a radius bisects a chord, then it bisects its arcs. (b) If a diameter bisects the major arc of a chord, then it is perpendicular to the chord. (c) If a diameter is perpendicular to a chord, it bisects the chord and its arcs.

(6.4)

Prove each of the following: (a) A radius through the point of intersection of two congruent chords bisects an angle formed by them.

Double-Declining Balance Double-declining balance is an accelerated method of depreciation be cause a greater amount of depreciation expense is taken in the early years of an asset s life and less is taken in later years. This method is preferred for the following reasons: = $.25 per mile

(6.4)





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(b) If chords drawn from the ends of a diameter make congruent angles with the diameter, the chords are congruent. (c) In a circle, congruent chords are equally distant from the center of the circle. (d) In a circle, chords that are equally distant from the center are congruent. 6.5. Determine each of the following, assuming t, t9, and t99 in Fig. 6-46 are tangents. (a) If mjA (b) If BR 90 in Fig. 6-46(a), what kind of quadrilateral is PAQO RC in Fig. 6-46(b), what kind of triangle is ABC (6.5)

(c) What kind of quadrilateral is PABQ in Fig. 6-46(c) if PQ is a diameter (d) What kind of triangle is AOB in Fig. 6-46(c)

Fig. 6-46

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In circle O, radii OA and OB are drawn to the points of tangency of PA and PB. Find mjAOB if mjAPB equals (a) 40 ; (b) 120 ; (c) 90 ; (d) x ; (e) (180 x) ; (f) (90 x) . (6.6) Find each of the following (t and t9 in Fig. 6-47 are tangents). In Fig. 6-47(a) (a) If mjPOQ (b) If mjPBO (c) If mjPAQ 80 , find mjPAQ. 25 , find mj1 and mjPAQ. 72 , find mj1 and mjPBO. (6.6)

Fig. 6-47

In Fig. 6-47(b) (d) If PB bisects jAPQ, find mj2. (e) If m j1 (f) If PQ 6.8. 35 , find mj2. QB, find mj1. (6.7)

1. Technology can make an asset obsolete or inadequate before the asset wears out. 2. Most plant assets decline in value more quickly in their early years than in later years. 3. Often, an asset contributes most to a business during its rst years. 4. The expenditure for equipment is made at the beginning of the asset s life. 5. It is good accounting practice to charge more depreciation in the early years of an asset s useful life. The double-declining balance method (DDB) produces the highest amount of depreciation in earlier years. It does not recognize scrap val ue. Instead, the book value of the asset remaining at the end of the de preciation period becomes the scrap value. Under this method, the straight-line rate is doubled and applied to the declining book balance each year. Many companies prefer the double-declining balance method because of the faster write-off in the earlier years when the asset con tributes the most to the business and when the expenditure was actually made. The procedure is to apply a xed rate to the declining book value of the asset each year. As the book value declines, the depreciation be comes smaller. For example, a $17,000 asset is to be depreciated over 5 years. The double-declining balance rate is thus 40 percent per year.

NOTATION, ENTITY,

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