Fun Geometry Problem with Solution #122
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٨ x = 6°
٨ 1



(1)∵∠BAC =∠ABC ∆ABC 繠∆˹Ҩ ՠ∠C ʹ BC = AC BC = BP

(2) AC ͡ѧش Q · AQ = AB
Ҡ∆APQ∆ABP ¤ѹẺ -- (AP = AP,∠PAQ =∠BAP, AQ = AB) PQ = BP
͡ҡ ѧҠ∠AQP =∠ABP ∠AQP = 2x

(3) ԨóҠ☐ABPQ Ҡ∠BPQ (˭) = 360°- 10x ∠BPQ () = 10x
ѧࡵ BC = BP Р∠CBP = 2(∠CQP) ش B 繨شٹҧͧǧՠ∆CPQ Ṻ BP = BQ
∴ BP = BQ = PQ ∆BPQ 繠∆ҹ ∠BPQ = 60° 10x = 60° x = 6° Q.E.D.


٨ 2(¤س Angel Lazo HK)



(1) ∵∠BAC =∠ABC ∆ABC 繠∆˹Ҩ ՠ∠C ʹ BC = AC BC = BP ∆BCP 繠∆˹Ҩ ՠ∠B (= 4x) ʹ ∠BCP (=∠BPC) = 90°- 2x

(2) ˹ش Q AB PQ⊥AB С˹ش R AC PR⊥AC
Ҡ∆APR∆APQ ¤ѹẺ -- (∠ARP =∠AQP,∠PAR =∠PAQ, AP = AP) PR = PQ

(3) ˹ش S CP BS⊥CP BS ǹ٧ͧ∆BCP CS = PS Р∠PBS (=∠CBS) = (∠CBP)/2 = 2x
Ҡ∆BPS∆BPQ ¤ѹẺ -- (∠BSP =∠BQP,∠PBS =∠PBQ, BP = BP) PS = PQ CS = PQ

(4) ѧࡵҠ∆CPR 繠∆ҡ ՠ∠R ҡ CP = 2‧PR ∠PCR = 30°
ԨóҠ∆ABC Ҡ∠BAC +∠ABC +∠ACB = 180° 6x + 6x + (120°- 2x) = 180° x = 6° Q.E.D.




Create Date : 22 ¹ 2558
Last Update : 22 ¹ 2558 0:00:00 .
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