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ssrs barcode font s 6. Corresponding parts of congruent ^ are >. in ObjectiveC
s 6. Corresponding parts of congruent ^ are >. Recognize Quick Response Code In ObjectiveC Using Barcode Control SDK for iPhone Control to generate, create, read, scan barcode image in iPhone applications. QR Code Generation In ObjectiveC Using Barcode generator for iPhone Control to generate, create QRCode image in iPhone applications. 6.4 Proving a circle problem stated in words Prove that if a radius bisects a chord, then it is perpendicular to the chord. Decode QR Code JIS X 0510 In ObjectiveC Using Barcode scanner for iPhone Control to read, scan read, scan image in iPhone applications. Generate Bar Code In ObjectiveC Using Barcode generation for iPhone Control to generate, create bar code image in iPhone applications. Solution
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The length of a tangent from a point to a circle is the length of the segment of the tangent from the given point to the point of tangency. Thus, PA is the length of the tangent from P to circle O in Fig. 616. Fig. 616 6.2A Tangent Principles
PRINCIPLE
A tangent is perpendicular to the radius drawn to the point of contact.
Thus if AB is a tangent to circle O at P in Fig. 617, and OP is drawn, then AB ' OP.
PRINCIPLE
A line is tangent to a circle if it is perpendicular to a radius at its outer end.
Thus if AB radius OP at P of Fig. 617, then AB is tangent to circle O.
Fig. 617 PRINCIPLE
Fig. 618 A line passes through the center of a circle if it is perpendicular to a tangent at its point of contact. Thus if AB is tangent to circle O at P in Fig. 618, and CP ' AB at P, then CP extended will pass through the center O. PRINCIPLE
Tangents to a circle from an outside point are congruent.
Thus if AP and AQ are tangent to circle O at P and Q (Fig. 619), then AP > AQ.
PRINCIPLE 5: The segment from the center of a circle to an outside point bisects the angle between the tangents from the point to the circle. Thus OA bisects j PAQ in Fig. 619 if AP and AQ are tangents to circle O.
Fig. 619 CHAPTER 6 Circles
6.2B Two Circles in Varying Relative Positions
The line of centers of two circles is the line joining their centers. Thus, OO9 is the line of centers of circles O and O9 in Fig. 620. Fig. 620 Fig. 621 Circles Tangent Externally Circles O and O9 in Fig. 621 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. 622 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. Fig. 622 Overlapping Circles Circles O and O9 in Fig.S 623 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. 624 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. 623 Fig. 624 CHAPTER 6 Circles
SOLVED PROBLEMS
6.5 Triangles and quadrilaterals having tangent sides Points P, Q, and R in Fig. 625 are points of tangency. Fig. 625 (a) In Fig. 625(a), if AP (b) In Fig. 625(b), if AP (c) In Fig. 625(b), if AP
OP, what kind of triangle is OPA PQ, what kind of triangle is APQ OP, what kind of quadrilateral is OPAQ (d) In Fig. 625(c), if OQ ' PR, what kind of quadrilateral is PABR
Solutions
(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

