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− | ==Theorem:==
| + | #REDIRECT [[Power of a Point Theorem]] |
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− | There are three unique cases for this theorem. Each case expresses the relationship between the length of line segments that pass through a common point and touch a circle in at least one point.
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− | ===Case 1 (Inside the Circle):===
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− | If two chords <math> AB </math> and <math> CD </math> intersect at a point <math> P </math> within a circle, then <math> AP\cdot BP=CP\cdot DP </math>
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− | ===Case 2 (Outside the Circle):===
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− | =====Classic Configuration=====
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− | =====Tangent Line=====
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− | ====Normal Configuration====
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− | ====Tangent Line====
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− | ===Case 3 (On the Border/Useless Case):===
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− | **Still working
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− | ==Proof==
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− | ==Problems==
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− | ====Introductory (AMC 10, 12)====
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− | ====Intermediate (AIME)====
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− | ====Olympiad (USAJMO, USAMO, IMO)====
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