Fun Geometry Problem with Solution #146



٨ x= 10°
٨ 1



(1)∠ACB = 80°

(2) ˹ش O circumcenter ͧ∆ABP ...
AO = BO = OP
∠AOP = 2(∠ABP) ∠AOP = 80°
∠BOP = 2(∠BAP) ∠BOP = 20°
∵ AO = BO ∆ABO 繠∆˹Ҩ ՠ∠O (= 100°) ʹ ∠BAO =∠ABO = 40°

BO = L OP = L

(3) BP ͡仾 AC ش Q ∠BQC = 80°
ѧࡵҠ∆ABQ∆ABO ¤ѹẺ -- (∠BAQ =∠BAO, AB = AB,∠ABQ =∠ABO) BQ = BO BQ = L
∵ ∠BQC =∠BCQ ∆BCQ 繠∆˹Ҩ ՠ∠B ʹ BC = BQ BC = L

(4) α= 10°
ѧࡵ ☐BCPO ՠBC = BO = OP,∠CBO = 120°- 2αР∠BOP = 2α ∠BCP =α (Click ʹԸվ٨⨷ 3) x = 10° Q.E.D.

٨ 2



(1) BP ͡仾 AC ش Q ∠APQ = 50° ∠BQC = 80°
∵ ∠BAQ =∠ABQ ∆ABQ 繠∆˹Ҩ ՠ∠Q ʹ AQ = BQ

BP = a PQ = b BQ = a + b AQ = a + b

(2) BQ ͡ѧش R · AR = a + b ∠AQR = 80°
∵ AQ = AR ∆AQR 繠∆˹Ҩ ՠ∠A ʹ ∠ARQ =∠AQR ∠ARQ = 80° ∠QAR = 20°

(3)∵∠PAR =∠APR ∆APR 繠∆˹Ҩ ՠ∠R ʹ PR = AR PR = a + b QR = a
Ҡ∆BCQ∆AQR ¤ѹẺ -- (∠CBQ =∠QAR, BQ = AQ,∠BQC =∠AQR) CQ = QR CQ = a

(4) ԨóҠ∆BCQ Ҡ∠B = 20°,∠Q = 80°ըش P BQ BP = CQ ∠BCP = 10° (Click ʹԸվ٨) x = 10° Q.E.D.




Create Date : 03 áҤ 2558
Last Update : 29 áҤ 2558 23:46:00 .
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