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Thus if PQ PR, where PQ and PR are the distances of P from the sides of j A in Fig. 4-25, then P is on AB, the bisector of jA.

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PRINCIPLE 5:



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The basic principles that apply to the sales journal also apply to the pur chases journal. However, a single-column purchases journal is too limit ed to be practicable, as businesses do not usually restrict their credit pur chases only to merchandise bought for resale. Various kinds of goods (of ce and store supplies, equipment) are bought on a charge basis. Therefore, the purchases journal can be expanded with special columns

Two points each equidistant from the ends of a line segment determine the perpendicular bisector of the line segment. (The line joining the vertices of two isosceles triangles having a common base is the perpendicular bisector of the base.)

Fig. 4-26

PRINCIPLE 6:

The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle.





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Thus if P is the intersection of the ' bisectors of the sides of ^ ABC in Fig. 4-27, then PA > PB > PC. P is the center of the circumscribed circle and is called the circumcenter of ^ABC.

Fig. 4-27

If a written-off account is later collected in full or part (a recovery of bad debts), the write-off will be reversed for the amount received. For example, after his account has been written off, Mr. Andrew pays his account in full. The reversing entry to restore his account will be: Accounts Receivable, John Andrew Allowance for Bad Debt 600

The bisectors of the angles of a triangle meet in a point which is equidistant from the sides of the triangle.

Thus if Q is the intersection of the bisectors of the angles of ^ ABC in Fig. 4-28, then QR > QS > QT, where these are the distances from Q to the sides of ^ABC. Q is the center of the inscribed circle and is called the incenter of ^ABC.

Fig. 4-28

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Finding distances In each of the following, find the distance and indicate the kind of distance involved. In4 4-29(a), Fig. 4 4 4 find the distance (a) from P to A; (b) from P to CD; (c) from A to BC; (d ) from AB to CD. In Fig. 4-29(b), find the distance (e) from P to inner circle O; (f) from P to outer circle O; (g) between the concentric circles.

Fig. 4-29

(a) PA (b) PG (c) AE (d) FG (e) PQ (f) PR (g) QR 7, distance between two points 4, distance from a point to a line 10, distance from a point to a line 6, distance between two parallel lines 12 3 12 5 5 3 9, distance from a point to a circle 7, distance from a point to a circle 2, distance between two concentric circles

Locating a point satisfying given conditions In Fig. 4-30. (a) Locate P, a point on BC and equidistant from A and C. (b) Locate Q, a point on AB and equidistant from BC and AC. (c) Locate R, the center of the circle circumscribed about ^ ABC. (d) Locate S, the center of the circle inscribed in ^ABC.

A separate entry will then be made in the cash receipts journal to record the collection, debiting Cash $600 and crediting Accounts Re ceivable, John Andrew. If a partial collection was made, the reversing en try should be made for the amount recovered.

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