zogfly3的部落格

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5條中5maths

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http://i293.photobucket.com/albums/mm67/zaza520/2011-12-11161230.jpg 31 http://i293.photobucket.com/albums/mm67/zaza520/2011-12-11161241.jpg 34 http://i293.photobucket.com/albums/mm67/zaza520/2011-12-11161250.jpg http://i293.photobucket.com/albums/mm67/zaza520/2011-12-11173109.jpg

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30a. angle BOC = 2 x angle BAC = 90 30b. consider triangle POQ tan OPQ = OQ/OP = 3/4 => angle OPQ = ... consider triangel POD sin OPQ = OD/OP = OD/5 => OD = ... 31a. PQ is a diameter of circle (let you proof) angle QRP = 90 (angle in semi-circle) and consider triangle ARP PR^2 = 9^2 + 15^2 => PR = ... 31b. triangle ARP similar to triangle APQ (AAA, but let you proof) AR/AP = RP/PQ = AP/AQ 9/15 = PR/PQ => PQ = .... 34a. consider triangle AOR: AO^2 = AR^2 + OR^2 => AR = 12 = AP 34b. PBQO is a square (let you proof) PB = BQ = 5 (AP+5)^2 + (5+CQ)^2 = (AP+CR)^2 (12+5)^2 + (5+CQ)^2 = (12+CR)^2 289 + 25 + 10CR + CR^2 = 144 + 24CR + CR^2 314 + 10CR = 144 + 24CR 170 = 14CR => CR = ... 1. join a line from A to D and B to C angle XBC = angle XDA ... triangle XAD is similar to triangle XCB XA/XC = AD/CB = XD/XB 6/XC = 5/10 XC = 12 DC = 7 2. draw a line from centre O to C and from centre O to A external angle COA = 200 internal angle COA = 160 consider quadrilateral ABCO: angle B = 360 - 90 - 90 - 160 = 20

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