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Circles Tangent Externally Circles O and O9 in Fig. 6-21 are tangent externally at P. AB 4 the common internal tangent of both circles. is The line of centers OO9 passes through P, is perpendicular to AB, and is equal in length to the sum of the radii, 4 R r. Also AB bisects each of the common external tangents, CD and EF. Circles Tangent Internally Circles O and O9 in Fig. 6-22 are tangent internally at P. AB is the common 4 external tangent of both circles. The line of centers OO9 if extended passes through P, is perpendicular to AB, and is equal in length to the difference of the radii, R r.



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Fig. 6-22

Overlapping Circles Circles O and O9 in Fig.S 6-23 overlap. Their common chord is AB. If the circles are unequal, their (equal) comS mon external tangents CD and EF meet at P. The line of centers OO9 is the perpendicular bisector of AB and, if extended, passes through P. Circles Outside Each Other Circles O and O9 in Fig. 6-24 are entirely outside each other. The common internal tangents, AB and CD meet at P. If the circles are unequal, their common external tangents, EF and GH if extended, meet at P9. The line of centers OO9 passes through P and P9. Also, AB CD and EF GH.

Fig. 6-23





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An offset (contra) account is an account with a credit balance that is offset against an asset account to produce the correct balance sheet book value The offset account appears in the general ledger directly after its companion account Generally, every depreciable asset has its own ac count and an accumulated depreciation account To determine the asset s book, or carrying, value, the accumulated depreciation account is sub tracted from the asset account..

Fig. 6-24

6.5 Triangles and quadrilaterals having tangent sides Points P, Q, and R in Fig. 6-25 are points of tangency.

Fig. 6-25

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OP, what kind of triangle is OPA PQ, what kind of triangle is APQ OP, what kind of quadrilateral is OPAQ

(a) AP is tangent to the circle at P; then by Principle 1, j OPA is a right angle. Also, AP is an isosceles right triangle. (b) AP and AQ are tangents from a point to the circle; hence by Principle 4, AP ^ APQ is an equilateral triangle. (c) By Principle 4, AP Then AP AQ OP AQ. Also, OP and OQ are > radii. And AP OP. Hence, ^ OAP PQ. Then

(d) By Principle 1, AP ' PR and BR ' PR. Then AP i BR, since both are ' to PR. By Principle 1, AB ' OQ; also, PR ' OQ (Given). Then AB i PR, since both are ' to OQ. Hence, PABR is a parallelogram with a right angle, or a rectangle.

2:3. 140 .

There is one exception to the above considerations: land. This xed asset is nondepreciable; it is usually carried on the books permanently at cost.

(c) In Fig. 6-26(c), DP and CQ are tangents. Find mj 2 and mj 3 if j OPD is trisected and PQ is a diameter.

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